Question

What are the coordinates of the endpoints of the midsegment for △ABC that is parallel to side BC?

Answer 1

Midpoint of segment AB = (-0.5, 5.5)
Midpoint of segment AC = (2, 3)
Those are the endpoints of the mid-segment parallel to side BC
They have the same slope

Answer 2

Coordinates of the endpoints of the mid segment for triangle ABC and parallel to side CB are ( -0.5 , 5.5 ) and ( 2 , 3 ).

Explanation:

Given a triangle ABC on coordinate plane.

Coordinates of the vertices are A( -4 , 2 ) , B( 3 , 9 ) and C( 8 , 4 )

To find: Coordinates of the endpoints of the mid segment for triangle ABC and parallel to side CB.

Mid segment means Line segment Joining the Mid-Points of the sides.

Converse of Mid-Point Theorem:

When a line is drawn from a mid point of a side of triangle and parallel to 2nd side then it bisects the third side of the triangle.

So, To find coordinates of the endpoint of line parallel to CB. We find Mid Points of the side AC and AB.

Mid point of AB =
`((-4+3)/(2),(2+9)/(2))=((-1)/(2),(11)/(2))=(-0.5,5.5)`

Mid point of AC =
`((-4+8)/(2),(2+4)/(2))=((4)/(2),(6)/(2))=(2,3)`

Therefore, Coordinates of the endpoints of the mid segment for triangle ABC and parallel to side CB are ( -0.5 , 5.5 ) and ( 2 , 3 ).