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

Question

The straight lines 7 x-2 y+10=0 and 7 x+2 y-10= 0 form an isosceles triangle with the line y=2. The area of this triangle is equal to (A) 15 / 7 sq. units (B) 10/7 sq. units (C) 18 / 7 sq. units (D) none of these

Tardigrade Admin · Accepted Answer

We have B ≡((6/7), 2), C ≡(-(6/7), 2) or B C=(12/7), A D=3 <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/200db141eb5216befc63ddb1b070a223-.png" /> ∴ ΔA B C=(1/2) × (12/7) × 3=(18/7) sq. units

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

$15/7$ sq. units

10/7 sq. units

$18/7$ sq. units

none of these

We have
$B \equiv (\frac{6}{7}, 2), C \equiv (- \frac{6}{7}, 2)$
or $BC = \frac{12}{7}, A D = 3$

$∴ Δ_{A BC} = \frac{1}{2} \times \frac{12}{7} \times 3 = \frac{18}{7}$ sq. units

Q. 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

15/7 sq. units