Question

Subject: Mathematics

Write the equation of the perpendicular bisector for segment BC and AC in triangle ABC with coordinates A(2, 3), B(0, 6), and C(2, 6).

a) \(y = -\frac{1}{2}x + 3\)

b) \(y = \frac{1}{2}x + 4\)

c) \(y = -\frac{1}{2}x + 5\)

d) \(y = \frac{1}{2}x + 3\)

Answer 1

To find the equation of the perpendicular bisector of segment BC, find the midpoint of segment BC, determine the slope of line BC, and write the equation of the perpendicular bisector.

Step-by-step explanation:

To find the equation of the perpendicular bisector of segment BC, we need to first find the midpoint of segment BC. The coordinates of point B are (0,6) and the coordinates of point C are (2,6). Using the midpoint formula, we can find the coordinates of the midpoint: M = ((x1+x2)/2, (y1+y2)/2). Substituting the coordinates of B and C, we have M = ((0+2)/2, (6+6)/2) = (1, 6).

Next, we need to find the slope of the line BC using the formula: m = (y2-y1)/(x2-x1). Substituting the coordinates of B and C, we have m = (6-6)/(2-0) = 0. Since the line BC is horizontal, the slope of the perpendicular bisector will be undefined.

Therefore, the equation of the perpendicular bisector of segment BC is x = 1, which represents a vertical line passing through the point (1,6).