Point E is located at (-2,3) and point F is located at (3,5). What is the distance between points E and F?

Answer 1

To solve this problem, you're going to want to use the distance formula:

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

Where "d" is the distance between the two points and

(x₁, y₁) = coordinates of the first point

(x₂, y₂) = coordinates of the second point

One thing to note here is that it doesn't matter which point is your "first" point and which point is your "second" point - you'll get the same answer either way.

So let's just keep it easy and make point E our first point and point F our second point:

First Point: (x₁, y₁) = (-2, 3)

Second Point: (x₂, y₂) = (3, 5)

Now, we substitute each value into the equation:

d = √[(3 - -2)² + (5 - 3)²)] = √(5^{2 +} 2²) = √29

So the distance between points E and F is √29 (the square root of 29)

Answer 2

distance between E and F = square root of ((5-3)^2 + (3+2)^2) = sqr(4+25) = sqr29

use the Pythagorean theorem

for (-2,3) and (3,5)

d^2 = (5-3)^2 + (3+2)^2 = 4+25 =29

d = sqr29 = about 5.385

It might help to plot the 2 points on a graph

if only to check if your calculations seem in the right range

Maybe plot the 2 points, then construct a right triangle

with base length 5, height length = 2, find the hypotenuse = square root of sum of squares of the 2 sides