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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 30,847

Hi,

CG#85. Find the value of k for which the points (7, -2), (5, 1), and (3, k) are collinear.

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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**Monox D. I-Fly****Member**- From: Indonesia
- Registered: 2015-12-02
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Actually I never watch Star Wars and not interested in it anyway, but I choose a Yoda card as my avatar in honor of our great friend bobbym who has passed away.

May his adventurous soul rest in peace at heaven.

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 30,847

Hi,

The solution CG#85 is correct. Excellent, Monox D. I-Fly!

CG#86. Find the value of k for which the points (8, 1), (k, -4), and (2, -5) are collinear.

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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**Monox D. I-Fly****Member**- From: Indonesia
- Registered: 2015-12-02
- Posts: 2,000

Actually I never watch Star Wars and not interested in it anyway, but I choose a Yoda card as my avatar in honor of our great friend bobbym who has passed away.

May his adventurous soul rest in peace at heaven.

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 30,847

Hi,

The solution CG#86 is correct. Excellent, Monox D. I-Fly!

CG#87. Find the distance between the points (0, 0) and (36, 15).

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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**Monox D. I-Fly****Member**- From: Indonesia
- Registered: 2015-12-02
- Posts: 2,000

Actually I never watch Star Wars and not interested in it anyway, but I choose a Yoda card as my avatar in honor of our great friend bobbym who has passed away.

May his adventurous soul rest in peace at heaven.

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 30,847

Hi,

The solution CG#87 is correct. Neat work, Monox D. I-Fly!

CG#88. Determine whether the points (1, 5), (2, 3), and (-2, -11)are collinear or not.

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

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**Monox D. I-Fly****Member**- From: Indonesia
- Registered: 2015-12-02
- Posts: 2,000

May his adventurous soul rest in peace at heaven.

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 30,847

Hi,

.

CG#89. Check whether (5, -2), (6, 4), and (7, -2) are the vertices of an isosceles triangle.

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

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 30,847

Hi,

CG#90. Find the values of y for which the distance between the points P(2, -3) and Q(10, y) is 10 units.

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

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 30,847

Hi,

CG#91. Find the area of a rhombus if its vertices are (3, 0), (4, 5), (-1, 4), and (-2, -1) taken in order. (Hint : Area of a rhombus = ½ x (product of its diagonals)).

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

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 30,847

Hi,

CG#92. Find the coordinates of a point A, where AB is the diameter of a circle whose center is (2,-3) and B is (1,4).

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

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**666 bro****Member**- From: Flatland
- Registered: 2019-04-26
- Posts: 328

Hi

Solution of CG#92 is A(3, -10).

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

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 30,847

Hi,

Excellent! The solution CG#92 is correct!

CG#93. Find the area of a triangle whose vertices are (-5, -1), (3, -5), and (5, 2).

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

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**666 bro****Member**- From: Flatland
- Registered: 2019-04-26
- Posts: 328

Cg#93 is 32 sq units

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

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 30,847

Hi,

The solution CG#93 is correct. Neat work!

CG#94. Find a relation between x and y if the points (x,y), (1,2), and (7,0) are collinear.

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

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**666 bro****Member**- From: Flatland
- Registered: 2019-04-26
- Posts: 328

Cg#94 is :x+3y=7.

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

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 30,847

Hi,

Neat work!

CG#95. Find the ratio in which the point (-3,p) divides the line segment joining the points (-5,-4) and (-2,3). Hence, find the value of p.

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

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**666 bro****Member**- From: Flatland
- Registered: 2019-04-26
- Posts: 328

CG#95. ∴ the ratio is 2:1 and the value of p =(2/3)

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

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 30,847

Hi,

Neat work!

CG#96. Find the value of k if the points A(2,3), B(4,k), and C(6,-3) are collinear.

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

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**666 bro****Member**- From: Flatland
- Registered: 2019-04-26
- Posts: 328

CG#96 The value of k=0

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

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 30,847

Hi,

Good work!

CG#97. The vertices of a triangle are (8,-4), (9,5), and (0,4). Prove that the triangle is an isosceles triangle.

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

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**666 bro****Member**- From: Flatland
- Registered: 2019-04-26
- Posts: 328

let the vertices of the triangle be labeled as A,B and C where

A =(8,-4)

B= (9,5)

and C=(0,4)

now ,distance of AB =

using distance formula = √( (x₂-x₁))^(2)+( (y₂-y₁) )^(2) )⃗, we get

=√( (9-8)^(2) )+(5+4)^(2) )

=√(82) units.

distance of BC = √( (0-9)^(2)+(4-5)^(2) )

= √(82) units

distance of AC = √( (8-0)^(2)+(4+4)^(2) )

= (8√(2)) units

∴ distance of ab = distance of bc = √(82) units

∆ABC is an isosceles triangle.

*Last edited by 666 bro (2020-06-18 02:02:57)*

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

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 30,847

The solution CG#97 is correct. Neat work!

CG#98. Find the co-ordinates of the mid-point of the line joining the points (-3,10) and (6,-8).

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

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**666 bro****Member**- From: Flatland
- Registered: 2019-04-26
- Posts: 328

Let the line joining points will be AB, where

A=(-3,10)

B=(6,-8)

let the coordinates of the mid point(m) will be =m(x,y)

now, midpoint of AB(m) =

using midpoint formula (m(x,y)) = ( (x₁+x₂)/2 , (y₁+y₂)/2 ) , we get

= ( (-3+6)/2 , ( 10-8)/2 )

m(x,y) = ( 3/2 , 1 )

∴ the coordinates of the midpoint (m) = ( 3/2 , 1)

*Last edited by 666 bro (2020-06-19 02:39:41)*

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

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