If a segment has an endpoint at (3, 2) and the midpoint at (-1, 2), what are the coordinates of the other endpoint?

3 Answers
nat
Apr 22, 2018

(-5,2)(−5,2)

Explanation:

The distance from the midpoint to the first endpoint is 44, which means that the other endpoint will be at the exact same distance from the midpoint as the first endpoint. So, four to the left of (-1,2)(−1,2) is (-5,2)(−5,2)

Barney V.
Apr 23, 2018

Coordinates of other endpoint=-5,2=−5,2

Explanation:

Let the first endpoint be AA and midpoint be BB and other endpoint be CC

Distance A to B:-

:.=sqrt((x_2-x_1)^2+(y_2-y_1)^2)

:.=sqrt(((-1)-(3))^2+(2-2)^2)

:.=sqrt((-4)^2+0

:.=sqrt(16)

:.=A to B=4units#

The segment is a vertical line because the y values of
A and B =2

Coords of B=-1,2

The bearing of the line B to C=180^@

:.cos 180^@=-1xx4.0=-4 add to x coord of B then

:.C=-5=x coord.

:.sin 180^@=0xx4.0=0 add to y coord of B then

:.C=2=y coord.

Coordinates of C=-5,2

Somebody N.
Apr 23, 2018

color(blue)((-5,2)

Explanation:

The coordinates of the midpoint of a line is given by:

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

Let the coordinates of the unknown end be:

(x_2 , y_2)

We know the coordinates of the midpoint are:

(-1,2)

So:

((3+x_2)/2,(2+y_2)/2)

And:

(3+x_2)/2=-1=>x_2=-5

(2+y_2)/2=2=>y_2=2

Coordinates:

(-5,2)

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