Question

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Find midsegment (EG) ̅ that is parallel to side (BC) ̅. Show all work to receive credit.

Answer 1

The coordinates of E are (-2,-1)and the coordinates of G are (1,0).

Explanation:

In a triangle, if a line connecting the midpoints of two sides then it is called a midsegment and that midsegment is parallel the third sides.

It is given that EG is parallel to BC, therefore E is the midpoint of BD and G is the midpoint of CD.

From the given figure it is noticed that the vertices of the triangle are B(-3,1), C(3,3) and D(-1,-3).

Midpoint formula

`midpoint=((x_1+x_2)/(2),(y_1+y_2)/(2))`

E is the midpoint of BD.

`E=((-3-1)/(2),(1-3)/(2))=(-2,-1)`

Therefore coordinates of E are (-2,-1).

G is the midpoint of CD.

`G=((3-1)/(2),(3-3)/(2))=(1,0)`

Therefore coordinates of G are (1,0).