Question

What are the endpoint coordinates for the mid segment of △PQR that is parallel to PQ?

Answer 1

Answer:

does it count when you put the decimal or does it have to be a fraction?

Step-by-step explanation:

Answer 2

Answer:

So the end points of the mid segment are:

S$(-3.5,0.5)$

T$(-1,-0.5)$

Step-by-step explanation:

First of all we need to list the co-ordinates of the points of the triangle shown.

P$\rightarrow(-3,3)$

Q$\rightarrow(2,1)$

R$\rightarrow(-4,-2)$

We need to find mid segment of the triangle which is parallel to segment PQ. This would mean we need to find midpoints of segment PR and QR and then join the points to get mid segment.

Midpoint Formula:

$(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

Midpoint of PR:

S($(\frac{-3+(-4)}{2},\frac{3+(-2)}{2})\\\\(\frac{-3-4}{2},\frac{3-2}{2})\\\\(\frac{-7}{2},\frac{1}{2} )$

S$(-3.5,0.5)$

Midpoint of QR:

T$(\frac{2+(-4)}{2},\frac{1+(-2)}{2})\\\\(\frac{2-4}{2},\frac{1-2}{2} )\\\\(\frac{-2}{2},\frac{-1}{2}$

T$(-1,-0.5)$

So the end points of the mid segment are:

S$(-3.5,0.5)$

T$(-1,-0.5)$

By mid segment theorem we know that the line joining midpoints of two sides of a triangle is parallel to the 3rd side.

∴ We know ST is parallel to PQ