Question

A line passes through the points (2, –2) and (–6, 2). The point (a, –4) is also on the line. What is the value of a?

Answer 1

Answer:

The value of a=6[/tex]

Step-by-step explanation:

step 1:-

col linearity of three points :-

We know that slopes of two parallel lines are equal.If two lines having the same slope pass through a common point ,then two lines will coincide . Hence ,If A,B,C are three points in the X Y- plane, then they will lie on a line,

that is three points are col linear if and only if Slope of AB= slope of BC

step 2:-

Since the given three points are col-linear, we have

Slope of AB= slope of BC

given points are A(2,-2) ,B(-6,2) and C(a,-4)

Step 3 :-

Slope of AB= slope of BC

$\frac{2-(-2)}{-6-2} =\frac{-4-2}{a+6}$

$\frac{-1}{2} =\frac{-6}{a+6}

 by cross multiplication

we get \\a+6=12\\

Step 4:-

The value of a=6$