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A B C D is a square A-=(1,2),B-=(3,-4)do...

`A B C D` is a square `A-=(1,2),B-=(3,-4)dot` If line `C D` passes through `(3,8),` then the midpoint of `C D` is (a) (2, 6) (b) `(6,2)` (c) `(2,5)` (d) `((28)/5,1/5)`

A

(2,6)

B

(6,2)

C

(2,5)

D

(28/5,1/5)

Text Solution

Verified by Experts

The correct Answer is:
D

`m_(AB) = (-4-2)/(3-1) = -3`
Thus, the equation of CD is y-8
=-3(x-3), i.e., y+3x=17. The equation of the right bisector of AB is
`y+1 = (1)/(3)(x-2)`
or 3y=x-5
Solving it with line CD, we get x=28/5, y=1/5. Thus, the midpoint of CD is (28/5,1/5).
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