First slide

Cartesian plane

Question

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

Moderate

A

l5/7 sq. units
B

10/7 sq. units
C

18/7 sq. units
D

None of these

Solution

We have
$\begin{aligned} B \equiv (\frac{6}{7}, 2), C \equiv (- \frac{6}{7}, 2) \\ or B C = \frac{12}{7}, A D = 3 \end{aligned}$
$∴ Δ_{A B C} = \frac{1}{2} \times \frac{12}{7} \times 3 = \frac{18}{7} sq. units$

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