X
25. If A(1, 2) and C(3, 8) are the extremities of a diagonal of the square ABCD, find the coordinates of
the other vertices
a) (5, 4) & (1,6) b) (5, 4) & (-1,6) c) (-5, 4) & (-1, 6) d) (-5,-4) & (-1,6)
bronch 11
3) find the
Answers
Answered by
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Step-by-step explanation:
The required circle will be a circle on the join of (-4,4) and (6,-1) as diameter whose equation is clearly
(x+4)(x−6)+(y−4)(y+1)=0
or x
2
+y
2
−2x−3y−28=0 ......(1)
Intercept on y-axis
=2
(f
2
−c)
=2
(
4
9
)+28
=11=AB
Putting X=0 in (1) the points A and B are given by
y
2
−3y−28=0or(y−7)(y+4)=0
∴ A(0,7), B(0,-4)
T
A
=2x−11y+77=0
T
B
=2x+11y+44=0
If they meet at C then C is (
4
−121
,
2
3
). Now we know the vertices of the triangle ABC and its area can be easily found out to be (
2
11
)
3
. Since the points A, B are y - axis and AB=11
∴Δ=
2
1
b×h=
2
1
⋅11×(
4
−121
)=(
2
11
)
3
numerically
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