Question

Show that lines x-2y - 7= 0 and 2x + y + 1 = 0 are perpendicular to each other. Find their point of intersection.​

Answer 1

• writing the equations in the form y = mx + c

y = x/2 -7/2. ;. y = -2x - 1

• slopes m1 = 1/2 ;. m2 = -2

• product of their slopes = m1 × m2 = 1/2 × -2 = -1
• since the product fo their slopes is -1 they are perpendicular to each other

• now equating the equations to get the point of intersection

(x/2) -(7/2) = -2x - 1

(1/2 + 2)x = 1 + 7/2

(5/2) x = 9/2

• x = 9/2 & finding value of y for this value of x.

y = -10 therefore point of intersection is (4.5 , -10)