Question

M is the midpoint of RS. R has coordinates (-2,-3) and M has coordinates (1,0). Find the coordinates of S.

Answer 1

Answer:

$(4,3)$

Step-by-step explanation:

Given

$R = (-2,-3)$

$M = (1,0)$

Required

Determine the coordinates of S

Midpoint is calculated as:

$M(x,y) = \frac{1}{2}(x_1 +x_2,y_1+y_2)$

Where:

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

$(x_1,y_1) = (-2,-3)$

Substitute these values in the above formula:

$(1,0) = \frac{1}{2}(-2 + x_2,-3+y_2)$

Multiply through by 2

$2 * (1,0) = 2 * \frac{1}{2}(-2 + x_2,-3+y_2)$

$(2,0) = (-2 + x_2,-3+y_2)$

By direct comparison:

$2 = -2 + x_2$ and $0 = -3 + y_2$

Solving for x2

$2 = -2 + x_2$

$x_2 = 2 + 2$

$x_2 = 4$

Solving for y2

$0 = -3 + y_2$

$y_2 = 0 + 3$

$y_2 = 3$

Hence, the coordinates of S is: $(4,3)$