which of the following points will be collinear with the points (-3, 4) and (2,-5)
Answers
Answer:
Consider the given points.
A(8,1),B(3,−4),C(2,−5)
If these three points are collinear, then slope of two pairs of points will be equal.
Slope of AB=
3−8
−4−1
=1
Slope of BC=
2−3
−5+4
=1
Slope of CA=
8−2
1+5
=1
Hence, the slope is the same. Hence, these three points are collinear.
Step-by-step explanation:
Correct Question
Which of the following points will be collinear with the points (-3, 4) and (2,-5)
a) (0,0)
b) (7, -14)
c) (0, -1)
d) (3, 1)
Answer
b) (7, -14) will be collinear with the points (-3, 4) and (2,-5).
Given
Points (-3, 4) and (2,-5)
To Find
The point that will be collinear
Solution
Let the third set of points be (x,y)
If the three points are collinear then,
the area between them should be 0.
Area of a triangle
Here,
x₁ = -3 x₂ = 2 x₃ = x
y₁ = 4 y₂ = -5 y₃ = y
Therefore,
1/2 | -3(-5 - y) + 2(y - 4) + x(4 -(-5)) | = 0
or, 1/2 | 15 + 3y + 2y - 8 + 9x | = 0
or, 1/2 | 7 + 5y +9x | = 0
or, | 7 + 5y +9x | = 0
or, 7 + 9x + 5y = 0
So now, we put the options into the equation obtained. If LHS = RHS then we get our answer.
For a)
We get 7, hence it is not the correct option.
For b)
7 + 9X7 + 5X(-14)
= 7 + 63 - 70
= 0
Hence, b) (7, -14) will be collinear with the points (-3, 4) and (2,-5).
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