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.

Given lines are : 3x + y = 4 ....(i) x- ay + 7 = 0 ....(ii) bx + 2y + 5 = 0 ....(iii) It's said that these lines form three consecutive sides of a rectangle. So, Lines (i) and (ii) must be perpendicular and also (ii) and (iii) will be perpendicular. Slope of line (i) is ⇒ 3x + y = 4 ⇒ y = -3x + 4. Comparing with y = mx + c we get, slope = m 1 = -3. Slope of line (ii) is ⇒ x - ay + 7 = 0 ⇒ ay = x + 7 ⇒ y = Comparing with y = mx + c we get, slope = m 2 = . Slope of line (iii) is ⇒ bx + 2y + 5 = 0 ⇒ 2y = -bx - 5 ⇒ y = Comparing with y = mx + c we get, slope = m 3 = . Since, lines (i) and (ii) are perpendicular so, ⇒ m 1 × m 2 = -1 Since, lines (ii) and (iii) are perpendicular so, ⇒ m 2 × m 3 = -1 Thus, the value of a is 3 and the value of b is 6.

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Mathematics

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.

Straight Line Eq

Related Questions

Is the line through (-2, 3) and (4, 1) perpendicular to the line 3x = y + 1? Does the line 3x = y + 1 bisect the join of (-2, 3) and (4, 1)?

The line through A(-2, 3) and B(4, b) is perpendicular to the line 2x - 4y = 5. Find the value of b.

Find the equation of a line, which has the y-intercept 4, and is parallel to the line 2x - 3y - 7 = 0. Find the coordinates of the point where it cuts the x-axis.

Find the equation of a straight line perpendicular to the line 2x + 5y + 7 = 0 and with y-intercept -3.