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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.
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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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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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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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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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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.
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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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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.
CG#89. Check whether (5, -2), (6, 4), and (7, -2) are the vertices of an isosceles triangle.
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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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.
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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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)).
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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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).
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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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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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).
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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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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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.
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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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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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.
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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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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Neat work!
CG#96. Find the value of k if the points A(2,3), B(4,k), and C(6,-3) 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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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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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.
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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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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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).
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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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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