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

9.25

Step-by-step explanation:

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

`((x_1+x_2)/(2),(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,

`((-6+2)/(2), (13+14)/(2))`

`=((-4)/(2),(27)/(2))`

`=(-2, 13.5)`

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

Then the coordinates of B are,

`((-6-2)/(2),(13+13.5)/(2))`

`=((-8)/(2), (26.5)/(2))`

`=(-4, 13.25)`

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