Question

JK is formed by J(-12,3) and K(8,-5). If line r is the perpendicular bisector of JK, write an equation for r in slope-intercept form.

Answer 1

• y = 5/2x + 4

Explanation:

Midpoint of JK:

• x = (-12 + 8)/2 = -4/2 = -2
• y = (3 - 5)/2 = -2/2 = -1

Slope of the line JK:

• m = (-5 - 3)/(8 - (-12)) = -8/20 = -2/5

Perpendicular lines have negative reciprocal slopes.

So the line r has a slope 5/2 and passes through the point (-2, -1)

Equation of r:

• y = 5/2x + b
• -1 = 5/2(-2) + b
• -1 = -5 + b
• b = 5 - 1
• b = 4

So the equation is:

• y = 5/2x + 4