Question

If the points A(x, 2), B (-3,-4) and C (7, -5) are collinear, then what is the value of x?

Answer 1

Step-by-step explanation:

Given:-

the points A(x, 2), B (-3,-4) and C (7, -5) are collinear.

To find:-

what is the value of x?

Solution:-

Given points are A(x, 2), B (-3,-4) and C (7, -5)

Given points are Collinear points.

We know that

If given points are Collinear points then the area of the triangle formed by the given points is zero.

The area of a triangle is formed by the points

(x1, y1) , (x2,y2) and (x3, y3) is

=∆=(1/2) | x1(y2-y3)+x2(y3-y1)+x3(y1-y2) | sq.units

We have

(1/2) | x1(y2-y3)+x2(y3-y1)+x3(y1-y2) | = 0

(x1, y1) = (x,2) => x1 = x and y1 = 2

(x2,y2) = (-3,-4) =>x2 = -3 and y2 = -4

(x3,y3) = (7,-5) =>x3 = 7 and y3 = -5

On Substituting the values in the above formula ,then

=>∆=(1/2) | x(-4-(-5))+(-3)(-5-2)+7(2-(-4)) | =0

=>∆=(1/2) | x(-4+5)+(-3)(-7)+7(2+4) | = 0

=>∆=(1/2) | x(1)+(21)+7(6) | = 0

=>∆=(1/2) | x+21+42| = 0

=>(1/2) | x+63 | = 0

=>(1/2)×(x+63) = 0

=>x+63 = 0×2

=>x+63 = 0

=>x = -63

The value of x = -63

Answer:-

The value of x for the given problem is -63

Used formula:-

• The points on the same line are called collinear points.
• If given points are Collinear points then the area of the triangle formed by the given points is zero.
• The area of a triangle is formed by the points x1, y1) , (x2,y2) and (x3, y3) is

∆=(1/2) | x1(y2-y3)+x2(y3-y1)+x3(y1-y2) | sq.units