Question

On a number line, the directed line segment from Q to S has endpoints Q at -2 and S at 6. Point R partitions the directed line segment from Q to S in a 3:2 ratio. Rachel uses the section formula to find the location of point R on the number line.

Answer 1

The answer to the question on ingenuity is 14/5

Answer 2

Using section formula, the coordinates of the point R on the number line is 2.8.

What is section formula?

Section formula is used to determine the point that divides a line segment joining two points into two parts such that the ratio of their length is m:n.

Given two points on a line segment P(x1) and Q(x2), and M be the point dividing the line-segment PQ internally in the ratio m:n,  then form the sectional formula for determining the coordinate of a point M is given by:

$M = \frac{mx2 + nx1}{m+n}$

Given line QS where Q = -2 and S = 6.

The ratio in which QS is divided by R = 3:2

Using the section formula to find R:

R = $\frac{3*6 + (-2)(2)}{3+2} = \frac{14}{5} = 2.8$

Learn more about section formula here

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