Question

A line segment has the endpoint T (2, 4) and the Midpoint of (3, 6.5) Find thecoordinates of the other point B. Write it as a point.

Answer 1

We have a segment, for which we know one endpoint T=(2,4) and the midpoint M=(3, 6.5).

We have to find the other endpoint, lets call it S.

Both for the x-coordinates and y-coordinates the distance in each axis from T to M (TM) has to be equal to the distance M to S (MS).

Then, if we look at the x-axis, we have that the distance is TMx=2-3=-1.

Then, S has to be one unit above M: the x-coordinate of S is xS=4.

We do the same for the y-axis. The distance TMy is TMy=4-6.5=-2.5.

Then, S has to be 2.5 units above M: the y-coordinate of S is yS=(6.5+2.5)=9.

The coordinates of S are (4,9).

Graph: