Question

Find the distance between the two points.

(4,3)
✓ [?]
Enter the number that
goes beneath the
radical symbol.

Answer 1

Answer: 89 will go in the box

This means the exact distance between the two given points is
`√(89)` which approximates to roughly 9.4339811

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Step-by-step explanation:

To get that answer, we can apply the distance formula

(x1,y1) = (-1,-5) is the first point

(x2,y2) = (4,3) is the second point

Plug the coordinates into the distance formula

`d = √((x_1 - x_2)^2 + (y_1 - y_2)^2)\\\\d = √((-1-4)^2 + (-5-3)^2)\\\\d = √((-5)^2 + (-8)^2)\\\\d = √(25 + 64)\\\\d = √(89)\\\\d \approx 9.4339811\\\\`

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Alternative Method:

You could also form a right triangle by adding the point (4, -5). The horizontal leg goes from (-1,-5) to (4,-5) which is a span of 5 units. The vertical leg goes from (4,-5) to (4,3) which is a span of 8 units. The hypotenuse is from (-1,-5) to (4,3) which is the distance we want to find.

After forming the triangle and determining the leg lengths, use the pythagorean theorem and you should get
`√(89)` as the length of the hypotenuse. As you can probably guess, the distance formula is effectively a slight rephrasing the pythagorean theorem.