If the equation of the hypotenuse of a right-angled isosceles triangle is 3 x + 4 y = 4 and its opposite vertex is 2,2 , then the equations of the perpendicular and the base are respectively

Question

If the equation of the hypotenuse of a right-angled isosceles triangle is 3 x + 4 y = 4 and its opposite vertex is 2,2 , then the equations of the perpendicular and the base are respectively, 7 x + y = 16 & x - 7 y + 12 = 0, 7 x - y = 12 & x + 7 y = 16, 5 x + y = 12 & x - 5 y + 8 = 0, x + 5 y = 12 & 5 x - y = 8

MARKS App · Accepted Answer

Let, the slope of the required line is m , then m - - 3 4 1 + m - 3 4 = ± tan ⁡ 45 o 4 m + 3 = ± 4 - 3 m ⇒ m = - 7 , 1 7 ⇒ equation of the lines are y - 2 x - 2 = - 7 & y - 2 x - 2 = 1 7 ⇒ 7 x + y = 16 & x - 7 y + 12 = 0

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