Exercise 12 Page 351

The midsegment triangle is a triangle formed by three midsegments. This means that its vertices are the midpoints of each side. We can find them using the Midpoint Formula. M(x_1+ x_2/2,y_1+ y_2/2) Let's begin with the side DE. Its endpoints are D(-3,1) and E(3,5).

M(x_1+ x_2/2,y_1+ y_2/2)

SubstitutePoints

Substitute ( -3,1) & ( 3,5)

M(-3+ 3/2,1+ 5/2)

AddTerms

Add terms

M(0/2,6/2)

CalcQuot

Calculate quotient

M(0,3)

The midpoint of DE has coordinates (0,3). We can use the same reasoning to find the midpoint of the other segments.

Side	Points	(x_1+x_2/2,y_1+y_2/2)	Midpoint
DE	( -3,1), ( 3,5)	(-3+ 3/2,1+ 5/2)	(0,3)
EF	( 3,5), ( 1,-5)	(3+ 1/2,5+( -5)/2)	(2,0)
DF	( -3,1), ( 1,-5)	(-3+ 1/2,1+( -5)/2)	(-1,-2)

Therefore, the coordinates of the vertices of the midsegment triangle of △ DEF are (0,3), (2,0), and (-1,-2).