First slide

Cartesian plane

Question

$A B C D$ is a square in which $A$ lies on the positive $y$ -axis and $B$ lies on the positive $x$ -axis. If $D$ is the point (12, 17), the coordinates of $C$ are

Moderate

A

(17, 12)
B

(17, 5)
C

(14, 16)
D

(15, 3)

Solution

Triangles $N D A, M B C$ and $O A B$ are congruent
$\Rightarrow M B = O A = N D = 12$
and $C M = O B = N A = O N - O A = 5$
$O M = O B + B M = 5 + 12 = 17$
coordinates of $C = (O M, C M) = (17, 5)$

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