Question

write the equation for the perpendicular bisector of B (6,6) and C (6,0) .

Answer 1

Write the equation for the perpendicular bisector of B (6,6) and C (6,0).

**Solution:**

1). The equation of the line passing through the points B and A

$$\frac{x - x_A}{x_B - x_A} = \frac{y - y_A}{y_B - y_A}$$ $$\frac{x - 6}{6 - 6} = \frac{y - 6}{0 - 6}$$ $$x = 6$$

This line is parallel to the y axis, so that the line is perpendicular to it must be parallel to the x-axis

2). If the point M is the midpoint of AB, then

$$x_M = \frac{x_A + x_B}{2} = \frac{6 + 6}{2} = 6$$ $$y_M = \frac{y_A + y_B}{2} = \frac{6 + 0}{2} = 3$$ $$M(6,3)$$

The equation of the line passing through the points M(6,3) and parallel to the x-axis is

$$y = 3$$