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#151 2020-06-19 12:43:02

ganesh
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Re: Coordinate Geometry

Solution CG#98 is correct. Good work!

CG#99. If the vertices of ΔABC are A(5,-1), B(-3,-2), and C(-1,8), find the length of the median through A.


It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi. 

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#152 2020-06-20 01:10:34

666 bro
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From: Flatland
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Re: Coordinate Geometry

The length of the median through A = √65 units.


"An equation for me has no meaning, unless it expresses a thought of God"- Srinivasa ramanujan

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#153 2020-06-20 16:05:22

ganesh
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Re: Coordinate Geometry

Hi,

Neat work!

CG#100. The point (4,2) divides the line segment joining (5,-1) and (2,y) in the ratio 1:2.


It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi. 

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#154 2020-06-21 02:01:15

666 bro
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Re: Coordinate Geometry

CG#100 : Let the points of the line segment will be AB, where
A = (5, -1)
B = ( 2 , y)
Let the point divides line segment will be C.
According to given conditions:
Point c divides line segment AB in the ratio 1:2
Coordinates of c (x, y) =     (4,2)
Using section formula =
                                        ((m₁x₂+m₂x₁)/(m₁+m₂) , (m₁y₂+m₂y₁)/(m₁+m₂))
where, x=4,  y=2 , x₁ = 5 ,  x₂ = 2 , y₁= -1, y₂ =y , m₁= 1 , m₂ =2                     

(4,2)  =   (   ( 2   +10) / (1+2)  , (y-2)/(1+2) )

(4,2)         =   (  4,  ( y-2)/3)   
          comparing corresponding y coordinates ,we get
2 =  ( y-2) /3   
6 = y-2
y= 8
   ∴  the value of y = 8.


"An equation for me has no meaning, unless it expresses a thought of God"- Srinivasa ramanujan

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#155 2020-06-21 13:38:23

ganesh
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Re: Coordinate Geometry

The solution CG#100 is correct. Good work!

CG#101. Find the mid-point of side BC of  ΔABC, with A(1,-4) and the mid-points of the sides through A being (2,-1) and (0,1).


It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi. 

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#156 2020-06-21 22:40:20

666 bro
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From: Flatland
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Posts: 244

Re: Coordinate Geometry

Given:∆ABC with midpoints of sides through A being (2,-1) and (0,1)
A = (1,-4)
let the midpoints are E & F, where
E = (2, -1)
F  = (0 ,1)
Let B = (x₂ , y₂)
Let  C = (x₃, y₃)
Let midpoint of BC will be = G
According to the given conditions:
Midpoint of AB = E
Using midpoint formula (m) =  (  (x₁+x₂)/2  , (y₁+y₂)/2  ) , we get
(2,-1) = (  (1+x₂)/2 , (-4+y₂)/2  )
Compairing  corresponding Coefficients , we get
(1+x₂)/2   = 2  and    (-4+y₂)/2   =-1
x₂+1=4       and          y₂-4 =-2
x₂ = 3      and  y₂ = 2
∴  B = (3,2) = (x₂,y₂)
similarly midpoint of AC = F
( (1+x₃)/2   , (-4+y₃)  )  =  ( 0,1)
( 1+x₃)/2 = 0  and (-4+y₃)/2  = 1
     x₃ =-1 and y₃ = 6
∴ c = ( -1,6) = (x₃,y₃)
now, midpoint of BC = G
  ( (x₃+x₂)/2 , (y₂+y₃)/2 ) = ( (-1+3)/2 ,  (6+2)/2 )
(1,4) =G
∴ the midpoint of BC(g) = (1,4)


"An equation for me has no meaning, unless it expresses a thought of God"- Srinivasa ramanujan

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#157 2020-06-22 00:05:07

ganesh
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Re: Coordinate Geometry

Hi,

The solution CG#101 is correct. Neat work!

CG # 102. Three consecutive vertices of a parallelogram are A(1,2), B(2,3), and C(8,5). Find the fourth vertex.


It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi. 

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#158 2020-06-22 22:01:28

666 bro
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From: Flatland
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Re: Coordinate Geometry

CG #102  the fourth vertex(D)  =  (7, 4)


"An equation for me has no meaning, unless it expresses a thought of God"- Srinivasa ramanujan

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#159 2020-06-23 00:14:08

ganesh
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Re: Coordinate Geometry

Hi,

CG # 103. Find the area of the quadrilateral whose vertices, taken in order, are (-4,-2), (-3,-5), (3,-2), and (2,3).


It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi. 

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#160 2020-06-23 17:16:22

666 bro
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From: Flatland
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Posts: 244

Re: Coordinate Geometry

CG#103: the area of quadrilateral is  = 28 sq units.


"An equation for me has no meaning, unless it expresses a thought of God"- Srinivasa ramanujan

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#161 2020-06-23 20:07:06

ganesh
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Re: Coordinate Geometry

Hi,

Good work!

CG # 104. Find the center of a circle passing through the points (6,-6), (3,-7), and (3,3).


It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi. 

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#162 2020-06-24 18:41:13

666 bro
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From: Flatland
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Re: Coordinate Geometry

CG#104 the center of the circle (h, k) = (3, -2)
The radius of the circle = 5 units
Equation of the circle
(x-3)^2 + ( y+2)^2  = 25.


"An equation for me has no meaning, unless it expresses a thought of God"- Srinivasa ramanujan

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#163 2020-06-24 19:59:15

ganesh
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Re: Coordinate Geometry

Neat work!

CG # 105. The two opposite vertices of a square are (-1,2), and (3,2). Find the coordinates of the other two vertices.


It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi. 

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#164 2020-06-25 20:15:28

666 bro
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From: Flatland
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Posts: 244

Re: Coordinate Geometry

The other two vertices are = (1, 2) and (1, 2) respectively.


"An equation for me has no meaning, unless it expresses a thought of God"- Srinivasa ramanujan

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#165 2020-06-26 00:07:36

ganesh
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Re: Coordinate Geometry

CG # 106. Determine the ratio in which the line 2x + y - 4 = 0 divides the line segment joining the point A(2,-2), and B(3,7).


It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi. 

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#166 2020-06-26 01:24:33

666 bro
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From: Flatland
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Re: Coordinate Geometry

CG#106:   The ratio(k:1) is = 2:9.


"An equation for me has no meaning, unless it expresses a thought of God"- Srinivasa ramanujan

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#167 2020-06-26 13:56:59

ganesh
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Re: Coordinate Geometry

Good work!

CG # 107. Find the coordinates of the points where a circle of radius √2, centered on the point with coordinates (1,1), cut the axes.


It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi. 

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#168 2020-06-26 23:08:24

666 bro
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From: Flatland
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Re: Coordinate Geometry

CG#107: the coordinates are (2, 0)  (0, 2) .


"An equation for me has no meaning, unless it expresses a thought of God"- Srinivasa ramanujan

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#169 2020-06-26 23:35:16

ganesh
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Re: Coordinate Geometry

Good work!

CG # 108. Calculate the length of the sides and diagonals of the quadrilateral A(-3,-2), B(-1,-2), C(0,0), and D(-3,1).


It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi. 

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#170 2020-06-27 17:02:22

666 bro
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From: Flatland
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Re: Coordinate Geometry

CG#108: ABCD is quadrilateral
where ,  A = (-3,-2)
                B = (-1,-2)
                 C = (0,0)
                  D = (-3,1)
AC & BD are diagonals
Now, using  distance formula = √( (x₂-x₁)^2 + (y₂-y₁)^2 ), we get
Distance of AB =   √( (-1+3)^2 +(-2+2) ^2)
                       AB     = 2 units.
Distance of BC  = √( (0+1)^2 + (0+2)^2)
                     BC  =   √(5) units.
distance of  CD  =  √( (-3+0)^2 +(1-0)^2)
                       CD = √(10) units.
  distance of  AD = √( (-3+3)^2 + (1+2) ^2)
                        AD = 3 units.
Distance of  diagonal AC = √( (0+3)^2 + (0+2)^2)
                                       AC = √(13) units.
distance of diagonal  BD  = √( (-3+1)^2+(1+2)^2)
                                       BD  = √(13) units.


"An equation for me has no meaning, unless it expresses a thought of God"- Srinivasa ramanujan

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#171 2020-06-27 18:27:26

ganesh
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Re: Coordinate Geometry

A transposing error!

CG # 109. Find the coordinates of the vertices of an equilateral triangle of side 2a.


It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi. 

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#172 2020-06-28 02:49:11

666 bro
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From: Flatland
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Posts: 244

Re: Coordinate Geometry

CG#109: the vertices are (0, ±√(3) ) , (-a,0) , (a,0) respectively.


"An equation for me has no meaning, unless it expresses a thought of God"- Srinivasa ramanujan

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#173 2020-06-28 13:31:01

ganesh
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Posts: 30,587

Re: Coordinate Geometry

Good attempt!

CG # 110. If the vertices of right angle triangle are (5,2), (2,-2), and (-2,a) and right angle between point (5,2) , (2,-2), and (2,-2), (-2,a), find the value of 'a'.


It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi. 

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#174 2020-06-28 22:31:43

666 bro
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From: Flatland
Registered: 2019-04-26
Posts: 244

Re: Coordinate Geometry

CG#110: the value of a = 1.

Last edited by 666 bro (2020-06-28 22:56:12)


"An equation for me has no meaning, unless it expresses a thought of God"- Srinivasa ramanujan

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#175 2020-06-30 14:55:55

ganesh
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Posts: 30,587

Re: Coordinate Geometry

Neat work!

(When questions on specific topics are posted, like coordinate geometry, algebra, mensuration etc., it may take some time to check and reply, say a fortnight or a month.)

CG # 111. If (-3,0) and (3,0) are two vertices of an equilateral triangle, find the coordinates of the third vertex.


It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi. 

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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