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

The value of a=6[/tex]

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

`(2-(-2))/(-6-2) =(-4-2)/(a+6)`

`(-1)/(2) =(-6)/(a+6) </p><p>  by cross multiplication </p><p>we get \\a+6=12\\</p><p><u><strong>Step 4:-</strong></u></p><p>The value of a=6`