First slide

Cartesian plane

Question

The straight line $7 x - 2 y + 10 = 0$ and $7 x + 2 y - 10 = 0$ forms an isosceles triangle with the line $y = 2,$ area of this triangle is equal to

Moderate

A

$15 / 7$ sq. units
B

$10 / 7$ sq. units
C

$18 / 7$ sq. units
D

7

Solution

We have, $A \equiv (0, 5), B \equiv (\frac{6}{7}, 2), C \equiv (- \frac{6}{7}, 2)$

$\Rightarrow$ $B C = \frac{12}{7}, A D = 3$

Area of $Δ A B C = \frac{1}{2} . \frac{12}{7} .3$ = $\frac{18}{7}$ sq. units

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