Question

Points M, R, and P are collinear on MP, and MR:RP=5/2. M is located at (-10,8), P is located at (-2,11) and R is located at (x,y). What are the values of x and y?

a) x = -6, y = 7
b) x = -4, y = 9
c) x = -8, y = 5
d) x = -5, y = 6

Answer 1

To find point R's coordinates we used the section formula with the ratio MR:RP being 5:2. The calculated coordinates for R are (-30/7, 71/7), which simplifies to (-4.2857, 10.1429). The closest answer choice is (b) x = -4, y = 9.

Step-by-step explanation:

The student has asked how to find the coordinates of point R, given that points M, R, and P are collinear on MP and MR:RP = 5:2. M is at (-10, 8) and P is at (-2, 11). To find the coordinates of R, we can use the section formula for internal division which is given by

( (m*x2 + n*x1) / (m + n), (m*y2 + n*y1) / (m + n) )

where x1, y1 and x2, y2 are the coordinates of points M and P respectively, and m and n are the respective ratios MR:RP (5 and 2).

Substituting the given values we get the coordinates of R as:

( (5*(-2) + 2*(-10)) / (5 + 2), (5*11 + 2*8) / (5 + 2) )

Which simplifies to:

( (-10 - 20) / 7, (55 + 16) / 7 )

( (-30) / 7, 71 / 7 )

( -30/7, 71/7 )

Therefore, the coordinates of point R are (-30/7, 71/7) which simplifies to (-4.2857, 10.1429). Based on the answer choices, the closest option to these values is (b) x = -4, y = 9.