First slide

Cartesian plane

Question

Consider a point $A (m, n),$ where m and n are positive integers.B is the reflection of A in the line $y = x, C$ is the reflection of B in the y-axis, D is the reflection of C in the x-axis and E is the reflection of D in the y-axis. The area of the pentagon $ABCDE$ is

Moderate

A

$2 m (m + n)$
B

$m (m + 3 n)$
C

$m (2 m + 3 n)$
D

$2 m (m + 3 n)$

Solution

Area of rectangle $BCDE = 4 mn$
Area of $ΔABC = \frac{2 m (m - n)}{2} = m^{2} - mn$
$∴$ Area of pentagon $\begin{array}{l} ABCDE = 4 mn + m^{2} - mn \\ = m^{2} + 3 mn \end{array}$

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