In the figure below, find the length of $¯ ¯¯¯ ¯ R S$ $bar(RS)$ if $¯ ¯¯¯¯ ¯ X Y$ $bar(XY)$ is a perpendicular bisector of $¯ ¯¯¯ ¯ T S$ $bar(TS)$ and $T R = 15 cm$ $TR = "15 cm"$ ?

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In the figure below, find the length of $¯ ¯¯¯ ¯ R S$ $bar(RS)$ if $¯ ¯¯¯¯ ¯ X Y$ $bar(XY)$ is a perpendicular bisector of $¯ ¯¯¯ ¯ T S$ $bar(TS)$ and $T R = 15 cm$ $TR = "15 cm"$ ?

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Answer 1 · 2018-07-01T00:15:15

$15 cm$ $"15 cm"$ .

If $¯ ¯¯¯¯ ¯ X Y$ $bar(XY)$ perpendicularly bisects $¯ ¯¯¯ ¯ T S$ $bar(TS)$ , it is perpendicular, meaning it is at a $90^{\circ}$ $90^@$ angle to $¯ ¯¯¯ ¯ T S$ $bar(TS)$ , and if it bisects, it divides in two. But if $¯ ¯¯¯¯ ¯ X Y$ $bar(XY)$ bisects $¯ ¯¯¯ ¯ T S$ $bar(TS)$ at a $90^{\circ}$ $90^@$ angle, then $¯ ¯¯¯¯ ¯ X Y$ $bar(XY)$ is also divided in two.

Therefore, the length of $¯ ¯¯¯ ¯ R S$ $bar(RS)$ is equal to the length of $¯ ¯¯¯¯ ¯ R X$ $bar(RX)$ , $¯ ¯¯¯¯ ¯ T R$ $bar(TR)$ , and $¯ ¯¯¯¯ ¯ R Y$ $bar(RY)$ .

As a result, if $¯ ¯¯¯¯ ¯ T R$ $bar(TR)$ is $15 cm$ $"15 cm"$ long, then the length of $¯ ¯¯¯ ¯ R S$ $bar(RS)$ is also $15 cm$ $"15 cm"$ .

CHALLENGE: What about the length of $¯ ¯¯¯¯ ¯ X Y$ $bar(XY)$ ? What would that be?

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In the figure below, find the length of $¯ ¯¯¯ ¯ R S$ $bar(RS)$ if $¯ ¯¯¯¯ ¯ X Y$ $bar(XY)$ is a perpendicular bisector of $¯ ¯¯¯ ¯ T S$ $bar(TS)$ and $T R = 15 cm$ $TR = "15 cm"$ ?

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In the figure below, find the length of bar(RS)¯¯¯¯¯RSbar(RS) if bar(XY)¯¯¯¯¯¯XYbar(XY) is a perpendicular bisector of bar(TS)¯¯¯¯¯TSbar(TS) and TR = "15 cm"TR=15 cmTR = "15 cm"?

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In the figure below, find the length of $¯ ¯¯¯ ¯ R S$ $bar(RS)$ if $¯ ¯¯¯¯ ¯ X Y$ $bar(XY)$ is a perpendicular bisector of $¯ ¯¯¯ ¯ T S$ $bar(TS)$ and $T R = 15 cm$ $TR = "15 cm"$ ?