ABCD is a square of with the co-ordinates of two opposite vertices A and C are (2,2) and (6,6) respectively. find the co-ordinates of B and D.
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Answers
Answer:
Solution
Let ABCD is a square where two opposite vertices are A(−1,2)andC(3,2).
Let B(x,y) and D(x1.y1) ids the other two vertices.
In Square ABCD
AB=BC=CD=DA
Hence AB=BC
⇒(x+1)2+(y−2)2=(3−x)2+(2−y)2 [by distance formula]
Squaring both sides
⇒(x+1)2+(y−2)2=(3−x)2+(2−y)2
⇒x2+2x+1+y2+4−4y=9+x2−6x+4+y2−4y
⇒2x+5=13−6x
⇒2x+6x=13−5
⇒8x=8
⇒x=1
In △ABC,∠B=90
Step-by-step explanation:
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Answer:
Let ABCD is a square where two opposite vertices are A(−1,2)andC(3,2).
Let B(x,y) and D(x1.y1) ids the other two vertices.
In Square ABCD
AB=BC=CD=DA
Hence AB=BC
⇒(x+1)2+(y−2)2=(3−x)2+(2−y)2 [by distance formula]
Squaring both sides
⇒(x+1)2+(y−2)2=(3−x)2+(2−y)2
⇒x2+2x+1+y2+4−4y=9+x2−6x+4+y2−4y
⇒2x+5=13−6x
⇒2x+6x=13−5
⇒8x=8
⇒x=1
In △ABC,∠B=90∘ [all angles of square are 90