Question

On a number line, the line segment from Q to S has endpoints Q at 79 and S at -51. Point R partitionsthe line segment from Q to Sin a 7:9 ratio. Find the location of point R accurate to two decimals.

Answer 1

First, we can model the situation as:

Because, we have two points S and Q, and a point in the middle R that divides the segment from Q to S in a ratio of 7:9. It means that if we divide the distance from RQ into the distance form SR, we are going to get 7/9.

Then, we can calculate the distance from S to Q as:

SQ = Q - S = 79 - (-51) = 130

Additionally, we can formulate the following equation:

SR + RQ = SQ

9x + 7x = 130

So, solving for x, we get:

16x = 130

x = 130/16

x = 8.125

Finally, point R can be calculated using the following equation:

R = S + 9x

R = - 51 + 9*(8.125)

R = -51 + 73.125

R = 22.125

The location of point R is 22.13

Answer: 22.13