Question

The straight line 7x – 2y + 10 = 0 and 7x + 2y – 10 = 0 forms an isosceles triangle with the line y = 2. Area of the triangle is equal to :

(a) (15/7) sq unit

(b) (10/7) sq unit

(c) (18/7) sq unit

(d) (10/13) sq unit

Answer 1

The correct option (c) (18/7) sq unit

Explanation:

lines 7x – 2y + 10 = 0, 7x + 2y – 10 = 0 & y = 2 forms isosceles triangle

lines 7x – 2y + 10 = 0, & y = 2 intersects in point [– (6/7)}, 2].

lines 7x – 2y + 10 = 0, & 7x + 2y – 10 intersects in point (0, 5)

lines 7x + 2y – 10 = 0, & y = 2 intersects in point [(6/7), 2].

= (1/2)|[{(12/7) + (12/7)} + 5{– (6/7) – (6/7)}]|

= (1/2)|[(24/7) – (60/7)]|

= (1/2) × (36/7)

= (18/7)sq. unit.