Question

Point C is the midpoint of AB.point A has coordinates (2,4)and point C has coordinates (5,0) what are the coordinates of point B?

Answer 1

Answer:

The coordinates of point B is (8,-4)

Step-by-step explanation:

Midpoint of a line segment: It is the point on the line segment that divides the segment in two congruent segments.

Since it is given that C is the midpoint of Line segment AB.

Mid-point of a segment of end points $A(x_{1},y_{1})$ and $B(x_{2},y_{2})$ is, C= $(\frac{x_{1}+x_{2}}{2} , \frac{y_{1}+y_{2}}{2})$.

As, given the coordinates of A and C are (2,4) and (5,0)

then,  we have $x_{1}=2$ , $y_{1}=4$ ; $\frac{x_{1}+x_{2}}{2}=5$  and $\frac{y_{1}+y_{2}}{2}=0$

to find the coordinates of $B(x_{2},y_{2})$.

$\frac{2+x_{2}}{2}=5$

Simplify:

$2+x_{2}=10$

⇒ $x_{2}=8$

to solve for $y_{2}$ we have, $\frac{y_{1}+y_{2}}{2}=0$

or $y_{1}+y_{2}=0$

or $y_{2}= -y_{1}$= -4

so, the values of $x_{2}=8$ and $y_{2}=-4$

Therefore, the coordinates of point B is (8,-4)