Perpendicular Bisectors

Front

What is a perpendicular bisector?

Back

A perpendicular bisector is a line that divides a segment into two equal parts at a 90-degree angle.

Front

How do you find the midpoint of a segment?

Back

The midpoint of a segment with endpoints (x1, y1) and (x2, y2) is given by the formula: \( \left( \frac{x1 + x2}{2}, \frac{y1 + y2}{2} \right) \).

Front

What is the relationship between a point on the perpendicular bisector and the endpoints of the segment?

Back

Any point on the perpendicular bisector is equidistant from the endpoints of the segment.

Front

If segment AB has endpoints A(2, 3) and B(6, 7), what is the midpoint?

Back

The midpoint is \( \left( \frac{2 + 6}{2}, \frac{3 + 7}{2} \right) = (4, 5) \).

Front

What is the slope of a line perpendicular to another line with slope m?

Back

The slope of a line perpendicular to another line with slope m is \( -\frac{1}{m} \).

Front

How do you determine if two lines are perpendicular?

Back

Two lines are perpendicular if the product of their slopes is -1.

Front

What is the distance formula used for?

Back

The distance formula is used to find the distance between two points (x1, y1) and (x2, y2): \( d = \sqrt{(x2 - x1)^2 + (y2 - y1)^2} \).

Front

If the length of segment TP is 7, what is the length of segment TQ if TQ is a perpendicular bisector?

Back

The length of segment TQ is also 7, as it is equal to the length of segment TP.

Front

What is the significance of the perpendicular bisector in triangle construction?

Back

The perpendicular bisector of a side of a triangle helps in finding the circumcenter, which is the center of the circumcircle.

Front

How can you verify if a point lies on the perpendicular bisector of a segment?

Back

To verify, check if the distances from the point to both endpoints of the segment are equal.