CIE iGCSE Maths E3.1 Coordinates Exam Style Practice Questions- Paper 2
Question
The diagram shows two sides of a parallelogram ABCD.
Find the coordinates of point D.
▶️Answer/Explanation
$(-3,7)$
In a parallelogram, the diagonals bisect each other
Midpoint formula
$
M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
$
$
M = \left( \frac{-7 + 3}{2}, \frac{5 + 3}{2} \right)
$
$
= (-2, 4)
$
Since diagonals bisect, point D should keep the midpoint the same
$
(-2, 4) = \left( \frac{-1 + x_D}{2}, \frac{1 + y_D}{2} \right)
$
$
-2 = \frac{-1 + x_D}{2}
$
$
x_D = -3
$
$
4 = \frac{1 + y_D}{2}
$
$
y_D = 7
$
$
D(-3, 7)
$