Final answer:
The equation of the perpendicular bisector of the segment with endpoints Q(-2, 0) and R(6, 12) is y = (-2/3)x + 10, found by calculating the midpoint of QR, the negative reciprocal of the slope of QR, and using the point-slope form.
Step-by-step explanation:
To find the equation of the perpendicular bisector of the line segment with endpoints Q(-2, 0) and R(6, 12), we need to follow several steps:
- Find the midpoint of the segment QR.
- Determine the slope of the line QR.
- Calculate the negative reciprocal of that slope to get the slope of the perpendicular bisector.
- Use the slope-point form to write the equation of the perpendicular bisector using the midpoint found in step 1 and the slope from step 3.
The midpoint M of QR is given by ((-2+6)/2, (0+12)/2) = (2, 6).
The slope of QR is (12-0)/(6-(-2)) = 12/8 = 1.5. The negative reciprocal of 1.5 is -2/3, which is the slope of the perpendicular bisector.
Now, using the point-slope form:
y - y₁ = m(x - x₁)
Where m is the slope of the perpendicular bisector and (x₁, y₁) is the midpoint M (2, 6).
y - 6 = (-2/3)(x - 2)
y = (-2/3)x + 4 + 6
y = (-2/3)x + 10
Therefore, the equation of the perpendicular bisector is y = (-2/3)x + 10.