Answer
M = [8.5, 2.16]
Explanation
Given:
A point M on a segment with endpoints X (1, -2) and Y (10, 3) partitions the segment in a 5:1 ratio.
What to find:
To find the value of M based on the information about the segment.
Solution:
Since segment XY is divided in the ratio of 5:1, that is, it is divided into 6 equal sections. (6 = 5 + 1).
m:n = 5:1
(x₁, y₁) = (1, -2)
(x₂, y₂) = (10, 3)
M can be calculated using the midpoint formula below:
[tex]M=[\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n}][/tex]Putting the values of the parameters into the formula, we have M to be equal:
[tex]\begin{gathered} M=[\frac{5\times10+1\times1}{5+1},\frac{5\times3+1\times-2}{5+1}] \\ \\ M=[\frac{50+1}{6},\frac{15-2}{6}] \\ \\ M=[\frac{51}{6},\frac{13}{6}] \\ \\ M=[8.5,2.16] \end{gathered}[/tex]Therefore, M = [8.5, 2.16]
