Answer:
Point A partitions MS in a 2:5 ratio.
Point K partitions MS in a 5:2 ratio.
Point R partitions MS in a 1:1 ratio.
Step-by-step explanation:
Point P(x,y) that partitions MS is a 2:5 ratio. I am going to draw the situation here.
Applying this, we can find the x and y coordinates of P.
x-coordinate:
x-coordinate of M is 2.
x-coordinate of P is x.
x-coordinate of S is 10.
Distance of MS: 10 - 2 = 8
Distance of MP: x - 2
Since the distance of MP is 2/7 of the distance of MS.
[tex]x-2=\frac{2}{7}\ast8[/tex][tex]x-2=\frac{16}{7}[/tex][tex]x=\frac{16}{7}+2=\frac{16}{7}+\frac{14}{7}=\frac{30}{7}[/tex]
Point A has x-coordinate of 30/7. So
Point A partitions MS in a 2:5 ratio.
Now, we want to find the point that partitions the segment in a 5:2 ratio. So
We want to find point P(x,y).
Now, we have to solve:
[tex]x-2=\frac{5}{7}\ast8[/tex][tex]x-2=\frac{40}{7}[/tex][tex]x=\frac{40}{7}+2=\frac{40}{7}+\frac{14}{7}=\frac{54}{7}[/tex]
Point K has x-coordinate 54/7. So
Point K partitions MS in a 5:2 ratio.
Finding the point that partitions in a 1:1 ratio.
Point P(x,y)
Then, we have to solve the following equation:
[tex]x-2=\frac{1}{2}\ast8[/tex]
So
x - 2 = 4
x = 6
Point R has x-coordinate equals to 6. So
Point R partitions MS in a 1:1 ratio.
