Math, asked by vikash8339, 4 months ago


which of the following points will be collinear with the points (-3, 4) and (2,-5) ​

Answers

Answered by Bloodrepr
4

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:

Answered by ChitranjanMahajan
2

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

= \frac{1}{2} | (x_{1} ( y_{2} - y_{3} )+x_{2}(y_{3}-y_{1}) +x_{3}(y_{1}-y_{2})|

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).

#SPJ2

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