Question

M(9, 8) is the midpoint of mc005-1.jpg The coordinates of S are (10, 10). What are the coordinates of R? a (8, 6) b (9.5, 9) c (11, 12) d (18, 16)

Answer 1

Let point R be (x₁, y₁) and Point S(10, 10) be (x₂, y₂)

Midpoint is given by $( \frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$

We know that the midpoint is (9, 8)
We will use this to evaluate the value of (x₁, y₁)

$\frac{x_1+x_2}{2}=9$
$\frac{x_1+10}{2}=9$
$x_1+10=18$
$x_1=8$

$\frac{y_1+y_2}{2}=8$
$\frac{y_1+10}{2}=8$
$y_1+10=16$
$y_1=6$

Point R (x₁, y₁) = (8, 6)

Correct answer: A