Question

Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar RS. is the perpendicular bisector of PQ . Point T is the midpoint of PQ . Point U lies on RS . If the length of UP is 7 units, the length of UQ is _____units.

Answer 1

As the first person was trying to say, but didnt really give the answer up front, the answer is 7 because UP=UQ.

The answer is 7.

Answer 2

We have that the answer is 7 units. A property of the perpendicular bisector of PQ (which can be used to define it) is that every point on it has the same distance from both P and Q. A proof of this is the following: Consider the shape if we join U with P and Q. There are 2 triangles, PTU and QTU. We have that the two T angles are 90 degrees, PT=TQ since T is the midpoint and the leg UT is common. Hence, by side-angle-side we have that the triangles are equal, hence UP=UQ