Question

Points $A$, $B$, $C$, and $D$ are located on a line. $A$ is at $(-6,13)$, $D$ is at $(2, 14)$, $C$ is the midpoint of $\overline{AD}$ and $B$ is the midpoint of $\overline{AC}$. What is the sum of the coordinates of point $B$

Answer 1

Answer:

9.25

Explanation:

∵ The coordinates of midpoint of a line segment having end points $(x_1,y_1)$ and $(x_2,y_2)$ are,

$(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

Given,

The coordinates of A are (-6, 13),

Coordinates of D are (2, 14),

If C is the midpoint of line segment AD,

Then the coordinates of C are,

$(\frac{-6+2}{2}, \frac{13+14}{2})$

$=(\frac{-4}{2},\frac{27}{2})$

$=(-2, 13.5)$

Now, if B is the mid point of line segment AC,

Then the coordinates of B are,

$(\frac{-6-2}{2},\frac{13+13.5}{2})$

$=(\frac{-8}{2}, \frac{26.5}{2})$

$=(-4, 13.25)$

Hence, the sum of the coordinates of B = -4 + 13.25 = 9.25