Try the fastest way to create flashcards
Question

# In the figure below, point Z is the image of point X resulting from successive reflections through parelle! lines, /, and /,. a - 11 Ne ee $\mathscr { A }$ a) Label the distance from X to /, 2 and the distance from ¥ to i, &. Also label the distances from Y to |, and Z to i, in terms of aand b. p) What is the distance between !, and f, in terms of @ and bb?

Solution

Verified
Step 1
1 of 3

a) Let $A$ be the intersection of $XY$ and $l_1$ and $B$ be the intersection of $YZ$ and $l_2$. Since $Y$ is $X$ reflected across $l_1$, then $XY\perp l_1$ and $XA=AY$. Since $Z$ is $Y$ reflected across $l_2$, then $YZ\perp l_2$ and $YB=BZ$. The distance from $X$ to $l_1$ is then $XA$ and the distance from $Y$ to $l_1$ is $AY$. Since these line segments are congruent, label them both as $a$. The distance from $Y$ to $l_2$ is $YB$ and the distance from $Z$ to $l_2$ is $BZ$. Since these line segments are congruent, label them both as $b$.

## Recommended textbook solutions

#### Geometry

1st EditionISBN: 9780076639298Carter, Cuevas, Cummins, Day, Malloy
4,575 solutions

#### enVision Geometry

1st EditionISBN: 9780328931583 (3 more)Al Cuoco
2,702 solutions

#### Big Ideas Math Geometry: A Common Core Curriculum

1st EditionISBN: 9781608408399 (1 more)Boswell, Larson
4,072 solutions

#### Big Ideas Math Geometry: A Common Core Curriculum

1st EditionISBN: 9781642087611Ron Larson
4,072 solutions