In a A B C , A B = A C where A is (3, 1) and the equation of the base B C is 2 x + y = 4 . Also, B lies on x + 3 y = 7 . Then sum of coordinates of vertex ' C ' is

Question

In a $∆ A B C, A B = A C$ where $A$ is (3, 1) and the equation of the base $B C$ is $2 x + y = 4$ . Also, $B$ lies on $x + 3 y = 7$ . Then sum of coordinates of vertex $' C'$ is ______

Smart Achievers · Accepted Answer

(4)

$B = (1, 2) & Let C \equiv (α, 4 - 2 α)$

$∴$ $A B = \sqrt{2^{2} + 1^{2}} = \sqrt{{(2 α - 3)}^{2} + {(3 - α)}^{2}},$

$5 α^{2} - 18 α + 13 = 0$

Solution

Q.
In a $∆ A B C, A B = A C$ where $A$ is (3, 1) and the equation of the base $B C$ is $2 x + y = 4$ . Also, $B$ lies on $x + 3 y = 7$ . Then sum of coordinates of vertex $' C'$ is ______

1 $\frac{13}{5}$

2 $\frac{18}{5}$

3 $\frac{16}{5}$

4 $\frac{7}{5}$

Ans.
(4)

$B = (1, 2) & Let C \equiv (α, 4 - 2 α)$

$∴$ $A B = \sqrt{2^{2} + 1^{2}} = \sqrt{{(2 α - 3)}^{2} + {(3 - α)}^{2}},$

$5 α^{2} - 18 α + 13 = 0$

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Solution

Q. In a ∆ABC, AB=AC where A is (3, 1) and the equation of the base BC is 2x+y=4. Also, B lies on x+3y=7. Then sum of coordinates of vertex 'C' is ______

1 135

2 185

3 165

4 75

Ans. (4) B=(1,2) & Let C≡(α,4-2α) ∴ AB=22+12=(2α-3)2+(3-α)2, 5α2-18α+13=0