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# find the distance between the points (5,4,) and (14,-2)

find the distance between the points (5,4)and(14,-2)

### 2 Answers by Expert Tutors

Jeffrey K. | Soar in Mathematics & SAT/ACT/ASVAB Prep - Home School Friendly!Soar in Mathematics & SAT/ACT/ASVAB Prep...
4.9 4.9 (300 lesson ratings) (300)
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Hi.  You could also use the distance formula to find the distance between two points.  For two points (x1, y1) and (x2, y2)  the distance between them is found with the following formula:

Distance = Square Root [ (x2 - x1)² + (y2-y1)²]  (i.e., the square root of the whole thing in brackets)

So in your problem, you would take Square Root [ (5 - 14)² + (4 - (-2))²]

= SR [ (-9)² + (6)²] = SR [81 + 36] = SR [117] ~  10.82

Luke B. | fun + learning = inevitable progressfun + learning = inevitable progress
4.9 4.9 (90 lesson ratings) (90)
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Use the Pythagorean Theorem:

"The sum of the squares of the sides equals the square of the hypotenuse."

(The square root of the square of the hypotenuse is what you are looking for.)

Basically think of your points as outlining a triangle. As far as setting up an equation, if your points are: (a, b) and (c, d), you get the distance with the theorem like this:

(d - b)+ (c - a)= distance2

You could also verify your answer by building a graph and measuring.