Question

2
Point M is the midpoint of line segment BC. If the coordinates of Mare (-1,1) and the coordinates of B are (3,4), find the coordinates of Point C
a(-5,-2)
b(7,7)
c(2,5)
b(1,5/2)

Answer 1

Answer:

a(-5,-2)

Step-by-step explanation:

The midpoint of a segment

Given points C(xc,yc) and B(xb,yb), the coordinates of the midpoint M can be found knowing that:

$\overline{CM} = \overline{ MB}$

Applying that relation in both axes separately, we can write:

$\displaystyle x_m=\frac{xc+xb}{2}$

$\displaystyle y_m=\frac{yc+yb}{2}$

Knowing the coordinates of the midpoint and B, we can find the coordinates of the other extreme C solving both equations for the required variable:

$x_c=2x_m-x_b$

$y_c=2y_m-y_b$

Plugging in the known values: M=(-1,1) and B=(3,4):

$x_c=2*(-1)-3=-2-3=-5$

$y_c=2*1-4 = 2-4=-2$

The coordinates of C are (-5,-2)

a(-5,-2)