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In an isosceles triangle ABC, the coordi...

In an isosceles triangle `ABC,` the coordinates of the points `B`and `C` on the base `BC` are respectively `(1, 2)` and `(2. 1).` If the equation of the line `AB` is `y= 2x,` then the equation of the line `AC` is

A

`y = (1)/(2) (x-1)`

B

`y = (x)/(2)`

C

`y = x - 1`

D

`2y = x +3`

Text Solution

Verified by Experts

The correct Answer is:
B
`/_ABC = tan theta = ((1)/(2)-1)/(1+(1)/(2)) =-(1)/(3) (m_(1) = (1)/(2),m_(2)=1)`
`:' AB = AC, :. /_ABC = /_ACB`

Hence, `-(1)/(3) = (m-1)/(1+m) rArr m =(1)/(2)` (here m is the gradient of line AC)
`:.` Equation of line AC is `y - 1 = (1)/(2) (x-2) rArr y =(x)/(2)`
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