Let $A B C D$ be 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.

(17, 12)

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(17, 5)

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(14, 16)

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(15, 3)

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Solution

The correct option is A $(17, 12)$
$F r o m f i g u r e$
$I n Δ A D M$
$l e t ∠ A D M = θ$
$t h e n ∠ M A D = 90 - θ$
$I n Δ A O B$
$∠ O A B = θ, ∠ O B A = 90 - θ$
$I n Δ C B N$
$∠ N B C = θ, ∠ B C N = 90 - θ$
$Δ A M D ≅ Δ B O A$
$Δ B O A ≅ Δ C N B$
$Sin c e D (12, 17)$
$i f M D = 12$
$t h e n A O = B N = 12$
$O M = 17$
$O A + A M = 17$
$A M = 5$
$A M = O B = C N = 5$
$H e n c e$
$O N = O B + B N$
$= 5 + 12 = 17$
$H e n c e C (17, 12)$

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Let ABCD be 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.

The correct option is A (17,12) Fromfigure InΔADM let∠ADM=θ then∠MAD=90−θ InΔAOB ∠OAB=θ,∠OBA=90−θ InΔCBN ∠NBC=θ,∠BCN=90−θ ΔAMD≅ΔBOA ΔBOA≅ΔCNB SinceD(12,17) ifMD=12 thenAO=BN=12 OM=17 OA+AM=17 AM=5 AM=OB=CN=5 Hence ON=OB+BN =5+12=17 HenceC(17,12)

Let $A B C D$ be 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.