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Find the distance between the points P(-...

Find the distance between the points P(-4, 7) and Q(2, -5).

A

`5`

B

`6`

C

`7`

D

6`sqrt5`

Text Solution

Verified by Experts

The correct Answer is:
D
The given points are P(-4, 7) and Q(2, -5).
Then, `x_(1) = -4, y_(1) = 7 "and"x_(2) = 2, y_(2) = -5`
`therefore PQ = sqrt((x_(2) -x_(1))^(2) + (y_(2) - y_(1))^(2))`
`= sqrt({2-(-4)}^(2) + (-5-7)^(2)) = sqrt(6^(2) + (-12)^(2))`
`=sqrt(36+144) = sqrt(180) = sqrt(36 xx 5) = 6sqrt(5)` units.
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