If a point lies on the perpendicular bisector AB then the point is equidistant from _________.

If a point lies on bisector of <RST, then the point is equidistant from _____

points A and B

lines SR and ST

If a point lies on the perpendicular bisector of segment AB, then the point is equidistant from point A and point B. This means that the point is the same distance away from point A as it is from point B.

To find the perpendicular bisector of segment AB, you need to follow these steps:
1. Determine the midpoint of segment AB. This can be done by finding the average of the x-coordinates and the average of the y-coordinates of points A and B.
2. Calculate the slope of segment AB using the formula: slope = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of points A and B.
3. Find the negative reciprocal of the slope calculated in step 2. This reciprocal is the slope of the perpendicular bisector.
4. Use the midpoint obtained in step 1 and the slope from step 3 to write the equation of the perpendicular bisector in point-slope form: y - y1 = m(x - x1), where (x1, y1) is the midpoint coordinates and m is the slope of the perpendicular bisector.

If a point lies on the bisector of angle RST, then the point is equidistant from the two rays that form angle RST. This means that the point is the same distance away from each of the two rays.

To find the bisector of angle RST, you need to follow these steps:
1. Draw rays starting from point R and passing through points S and T.
2. Using a compass, draw arcs on both rays with the same radius, starting from points S and T.
3. The point where these arcs intersect is the point on the bisector of angle RST.
4. Draw a line passing through this point and point R. This line is the bisector of angle RST.

Remember, equidistant means the same distance. So, if a point lies on a perpendicular bisector, it is equidistant from the two endpoints of the line segment. Similarly, if a point lies on the bisector of an angle, it is equidistant from the two rays that form the angle.