Question

point p bisects a line segment AB. P lies at (3,-3/2a) . A lies at (-4-a/2,-2a) and B lies at (20+3a,-a) find the value of a?​

Answer 1

Answer:

P is (3, -3/2) if a=1 or (3, 3/2) if a=-1

Step-by-step explanation:

When a point bisects a line segment, it divides the line into two equal parts, i.e., the point is the midpoint of the line segment.

So, point P is the midpoint of the line segment AB.

According to bisection formula,

a midpoint c is calculated as the arithmetic mean between points a and b and is given by c=(a+b)/2

Therefore, P=(A+B)/2

or, 3=(-4-a/2+20+3a)/2 , -3/2a=(-2a-a)/2

Solving any one of the equation will give the value of a.

Here, taking the second equation,

-3/2a=(-2a-a)/2

or, -3/2a=-3a/2

or, -6=-6a^2

or, a^2=1

or, a=±1

Hence, the point P is (3, -3/2) if a=1 or (3, 3/2) if a=-1.