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 line segment?

Back

To find the midpoint of a line segment with endpoints (x1, y1) and (x2, y2), use the formula: Midpoint = ((x1 + x2)/2, (y1 + y2)/2).

Tags

CCSS.HSG.GPE.B.6

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.

Tags

CCSS.HSG.CO.C.9

Front

How can you determine if a line is a perpendicular bisector of a segment?

Back

A line is a perpendicular bisector if it intersects the segment at its midpoint and forms right angles with the segment.

Front

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

Back

The slope of a line that is perpendicular to another line with slope m is -1/m.

Tags

CCSS.HSG.CO.A.1

Front

If GH = 8 and CH = 12, what is the total length of segment GC?

Back

The total length of segment GC is GH + CH = 8 + 12 = 20.

Front

How do you solve for x in an equation involving perpendicular bisectors?

Back

To solve for x, set up an equation based on the properties of the perpendicular bisector, such as equidistance from endpoints.

Tags

CCSS.HSG.CO.C.9

Front

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

Back

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

Tags

CCSS.HSG.CO.C.9

Front

What is the formula for the distance between two points (x1, y1) and (x2, y2)?

Back

The distance formula is: Distance = √((x2 - x1)² + (y2 - y1)²).

Tags

CCSS.HSG.GPE.B.7

Front

How can you verify if two segments are equal using perpendicular bisectors?

Back

You can verify if two segments are equal by showing that their endpoints are equidistant from a point on the perpendicular bisector.

Tags

CCSS.HSG.CO.C.9