AOBC is a rectangle whose three vertices are A(0,3) O(0,0) B(5,0) Find coordinate of C through Distance formula - Maths - Coordinate Geometry

Question

AOBC is a rectangle whose three vertices are A(0,3) O(0,0) B(5,0)
Find coordinate of C through Distance formula

Neha Sethi · Accepted Answer

Dear student
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Let the coordinates of C be x,y In a rectangle opposite sides are equal
⇒AC=OB and AO=CB⇒Distances between them is also equal
Distance between OB=Distance between ACDistance between OB=5-02+0-02  using distance formula=25=5 units
=Distance between AC⇒x-02+y-32=5Squaring both sides, we getx-02+y-32=25x2+y2+9-6y=25x2+y2+9-6y-25=0x2+y2-16-6y=0  
1Now, Distance between OA=0-02+3-02  using distance formula=9=3 units
= Distance between BC⇒x-52+y-02=3Squaring both sides, we getx-52+y-02=9x2+25-10y+y2-9=0x2+y2-10y+16=0 
2Subtracting 2 from 1, we getx2+y2-16-6y-x2+y2-10y+16=0x2+y2-16-6y-x2-y2+10y-16=0-16-6y+10y-16=04y=3y=8Consider, x-02+y-32=25Put y=8x-02+8-32=25x2=25-25x=0So, coordinates are 0,8
Regards

AOBC is a rectangle whose three vertices are A(0,3) O(0,0) B(5,0). Find coordinate of C through Distance formula.