# math Given P(7,11) and Q(-2,4), find what are length, slope and the midpoint of segment passing through the points?

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We have the points P(7,11) and Q(-2,4), and we need to find the length, slope and the midpoint of the line segment joining them.

The length of the line segment is: sqrt ((7 + 2)^2 + (11 - 4)^2)

=> sqrt(9^2 + 7^2)

=> sqrt(81 + 49)

=> **sqrt (130)**

The slope of the line segment is (4 - 11)/(-2 - 7) = -7/-9 = **7/9**

The mid point of the line segment is ((7 - 2)/2 , (11 + 4)/2)

or **(2.5 , 7.5)**

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

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

[PQ] = sqrt[(-2-7)^2 + (4-11)^2]

[PQ] = sqrt (81 + 49)

[PQ] = sqrt 130

The slope of the line PQ is:

mPQ = (yQ-yP)/(xQ-xP)

mPQ = (4-11)/(-2-7) => mPQ = -7/-9 => mPQ = 7/9

The midpoint of the line PQ is :

xM = (xP + xQ)/2

xM = (7-2)/2 => xM = 5/2

yM = (yP + yQ)/2 => yM = (11+4)/2 => yM = 15/2

The requested coordinates of the midpoint are: M(5/2 ; 15/2).