# What is the length of the segment with endpoints P(8,-7) and Q(8,10)?

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We are given the end points P and Q of the segment. The points are P(8,-7) and Q(8,10).

Now the distance between the points (x1, y1) and (x2, y2) is equal to sqrt [( x2- x1)^2 + (y2 - y1)^2]

Substituting the values we have here, we get the distance PQ as

sqrt [( 8 - 8)^2 + ( 10 + 7)^2]

=> sqrt (17^2)

=> 17

**Therefore the required length of the segment PQ is 17.**

The length of the segment PQ could be calculated using the formula:

[PQ] = sqrt[(xP - xQ)^2 + (yP - yQ)^2]

We'll substitute the coordinates of P and Q in the formula above:

[PQ] = sqrt[(8 - 8)^2 + (-7-10)^2]

We'll compute and we'll get:

[PQ] = sqrt[(0)^2 + (-17)^2]

[PQ] = sqrt[(-17)^2]

[PQ] = 17 units

**The length of the segment PQ, whose endpoints are P(8,-7) and Q(8,10), is [PQ] = 17 units.**