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**Jai Ganesh****Administrator**- Registered: 2005-06-28
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Hi,

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

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

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
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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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**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 48,286

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 appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

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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**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 48,286

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 appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

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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**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 48,286

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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**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 48,286

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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**Jai Ganesh****Administrator**- Registered: 2005-06-28
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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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**Jai Ganesh****Administrator**- Registered: 2005-06-28
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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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**Jai Ganesh****Administrator**- Registered: 2005-06-28
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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
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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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**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 48,286

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
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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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**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 48,286

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
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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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**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 48,286

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
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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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**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 48,286

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: 706

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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**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 48,286

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: 706

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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**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 48,286

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
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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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