# If the lines 3x+y=4, x-ay+7=0 and bx+2y+5=0 form three consecutive sides of a rectangle, find the values of a and b.

1
Log in to add a comment

Log in to add a comment

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.

L1: 3 x + y = 4

L2: x - a y + 7 = 0

L3: b x + 2 y + 5 = 0

L1 || L3 => the coefficients of x and y in L1 and L2 are proportional or, the slopes of the two lines are equal.

3 : b = 1 : 2 => b = 6

L1 Perpendicular to L2. The product of the slopes is -1.

-3 * 1/a = -1 => a = 3

L2: x - a y + 7 = 0

L3: b x + 2 y + 5 = 0

L1 || L3 => the coefficients of x and y in L1 and L2 are proportional or, the slopes of the two lines are equal.

3 : b = 1 : 2 => b = 6

L1 Perpendicular to L2. The product of the slopes is -1.

-3 * 1/a = -1 => a = 3