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40 votes
40 votes
What is the distance between (-2, 4) and (5, 4) on a coordinate grid?

1 Answer

22 votes
22 votes

Answer:

7 units

Explanation:

(Background info, skip if not interested or needed for you)

The equation for distance on a cartesian plane coordinate system is based off the pythagorean theorem.


a^2 + b^2 = c^2

a and b being sides of a right triangle, c being the hypotenuse.

When we are solving for distance we are solving for c essentially.


c =
√(a^2 + b^2)

Because a and b are side lengths of the right triangle, we need to find a way to find that in terms of coordinates. So here we might say that a is equal to the horizontal distance between the 2 points or Δx, and we would say that b is the vertical distance between the 2 points Δy.

(solutions)

So essentially distance is:


d = √((x_2 - x_1)^2+ (y_2-y_1)^2 )

Now we just use the values given to us, and sub in the x and y values respectively.

(-2,4)
x_1 = -2, y_1 = 4

(5,4)
x_2 = 5, y_2 = 4

plug these values in:


d = √(((5) - (-2))^2+ (4-4)^2 ) = √((7)^2+ (0)^2 ) = √(7^2 ) = 7

Therefore the distance is 7 units.

User Bluelurker
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