Question

Find the coordinates of the missing endpoint if W is the MIDPOINT of XY.

W(4,-2) X(7,-4)

Answer 1

Answer:

The coordinates of the missing point if W is the midpoint of XY is $Y(x,y) =(1,0)$.

Explanation:

From Linear Algebra we define the location of midpoint by the following expression:

$W(x,y) = \frac{1}{2}\cdot X(x,y)+\frac{1}{2}\cdot Y(x,y)$ (1)

Where:

$X(x,y)$, $Y(x,y)$ - Endpoints of the line segment, dimensionless.

$W(x,y)$ - Midpoint, dimensionless.

If we know that $W(x,y) =(4,-2)$ and $X(x,y) = (7,-4)$, then the location of the point Y is:

$Y(x,y) = 2\cdot W(x,y) -X(x,y)$

$Y(x,y) = 2\cdot (4,-2)-(7,-4)$

$Y(x,y) = (8,-4)-(7,-4)$

$Y(x,y) =(8-7,-4+4)$

$Y(x,y) =(1,0)$

The coordinates of the missing point if W is the midpoint of XY is $Y(x,y) =(1,0)$.