Question

IfP(a/3,4)is the mid-point of the line segment joining the points Q(-6,5)and R(-2,3), then find the value of'a'."

Answer 1

a = -12

Explanation:

We can find the equation that describes the points Q and R, assuming they form a straight line. Find the slope, or Rise/Run, between these two points:

Going from(-6,5) to (-2,3):

Rise = (3-5) = -2

Run = (-2 - (-6)) = 4

Slope (Rise/Run) = (-2/4 or -(1/2)

The equation takes the form of y = -(1/2)x + b

Find b by using one of the two points. Lets use (-2,3):

y = -(1/2)x + b

3 = -(1/2)(-2) + b for (-2,3)

3 = 1 + b

b = 2

The equation of the two points Q and R is:

y = -(1/2)x + 2

We want to find the point on this line described only as P (a/3,4). Lets use the equation to find the value of x when y=4:

y = -(1/2)x + 2

4 = -(1/2)x + 2 for y=4

2 = -(1/2)x

x = -4

Point P is (-4,4)

For P (a/3,4) to be true,

a/3 = -4

a = -12