## Related questions with answers

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

VerifiedStep 1

1 of 3a) 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 $b$.

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