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Geometry

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Segment PQ is the perpendicular bisector of Segmetn ST. Find the values of m and n.

Segment SP = 3m + 9                           Segment SQ = 6n -3

Segment PT = 5m - 13                          Segment TQ = 4n + 14

m=11 n=8.5

off-topic
Jan 24, 2018
edited by NiteWolf813  Jan 24, 2018
edited by NiteWolf813  Jan 24, 2018
edited by NiteWolf813  Jan 24, 2018

#1
+2338
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In this case, we can utilize the perpendicular bisector theorem, which states that $$\overline{SP}\cong\overline{PT}$$. Therefore, set the measure of them equal to each other to figure out the unknown.

 $$SP=PT$$ We know the length of these segments already. $$3m+9=5m-13$$ Subtract 2m from both sides first. $$9=2m-13$$ Add 13 to both sides. $$22=2m$$ Divide by 2 from both sides to isolate the variable completely. $$11=m$$

Using the same logic as before, we also know that $$\overline{SQ}\cong\overline{TQ}$$.

 $$SQ=TQ$$ Use substitution here! $$6n-3=4n+14$$ Subtract 4n from both sides. $$2n-3=14$$ Add 3 to both sides. $$2n=17$$ Divide by 2 from sides to isolate the unknown completely. This process is exactly the same as the first one. $$n=\frac{17}{2}=8.5$$
Jan 24, 2018

#1
+2338
+2

In this case, we can utilize the perpendicular bisector theorem, which states that $$\overline{SP}\cong\overline{PT}$$. Therefore, set the measure of them equal to each other to figure out the unknown.

 $$SP=PT$$ We know the length of these segments already. $$3m+9=5m-13$$ Subtract 2m from both sides first. $$9=2m-13$$ Add 13 to both sides. $$22=2m$$ Divide by 2 from both sides to isolate the variable completely. $$11=m$$

Using the same logic as before, we also know that $$\overline{SQ}\cong\overline{TQ}$$.

 $$SQ=TQ$$ Use substitution here! $$6n-3=4n+14$$ Subtract 4n from both sides. $$2n-3=14$$ Add 3 to both sides. $$2n=17$$ Divide by 2 from sides to isolate the unknown completely. This process is exactly the same as the first one. $$n=\frac{17}{2}=8.5$$
TheXSquaredFactor Jan 24, 2018