Question

lesson 1.3 practice b for use with pages 15–22 1. line rs bisects $overline{pq}$ at point r. find rq if pq = 14 centimeters. 2. line jk bisects $overline{mn}$ at point j. find mn if $jm = 6\frac{3}{4}$ feet. 3. point t bisects $overline{uv}$. find uv if $ut = 4\frac{1}{2}$ yards. 4. point c bisects $overline{ab}$. find cb if ab = 14.8 meters.

Explanation:

Problem 1

Step1: Recall bisect definition

If a line bisects a segment at a point, the point divides the segment into two equal parts. So \( PR = RQ \) and \( PQ = PR + RQ = 2RQ \).

Step2: Solve for \( RQ \)

Given \( PQ = 14 \) cm, then \( RQ=\frac{PQ}{2}=\frac{14}{2} = 7 \) cm.

Step1: Recall bisect definition

If \( JK \) bisects \( \overline{MN} \) at \( J \), then \( JM = JN \) and \( MN = JM + JN = 2JM \).

Step2: Calculate \( MN \)

Given \( JM = 6\frac{3}{4}=\frac{27}{4} \) feet, so \( MN = 2\times\frac{27}{4}=\frac{27}{2}=13\frac{1}{2} \) feet.

Step1: Recall bisect definition

If \( T \) bisects \( \overline{UV} \), then \( UT = TV \) and \( UV = UT + TV = 2UT \).

Step2: Calculate \( UV \)

Given \( UT = 4\frac{1}{2}=\frac{9}{2} \) yards, so \( UV = 2\times\frac{9}{2}=9 \) yards.

Answer:

\( 7 \) centimeters

Problem 2