Question

ABCD is a square in which A lies on positive y-axis and B lies on the positive x-axis .If D is the point (12,17), then co-ordinate of C is:

Answer 1

Abcd is a square in which a lies on positive yaxis and blies on positive xaxis

Answer 2

Answer: C(17,12)

Concept: All angles of a square are of 90 degrees

All sides of square are equal.

Given: ABCD is a square in which A lies on positive y-axis and B lies on the positive x-axis

D (12,17)

To find: Co ordinates of point C

Step-by-step explanation:

Here we use the concept of trigonometry and theory of congruent triangles to find the Co ordinates of point C.

Co ordinate geometry is the study of points in the plane.

From figure

InΔADM

let∠ADM=θ

then∠MAD=90−θ

InΔAOB

∠OAB=θ,∠OBA=90−θ

I

nΔCBN

∠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

Hence C(17,12)

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