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Chapter 4: Problem 1

Find the distance between the points (3,-2) and (-1,4) .

Short Answer

Expert verified
The distance between the points (3,-2) and (-1,4) is \( d = 2\sqrt{13} \).

Step by step solution

01

Write down the coordinates of the points

The given points are (3,-2) and (-1,4).
02

Identify the coordinates of each point

Let's assign the coordinates of each point like this: Point A: (x1, y1) = (3, -2) Point B: (x2, y2) = (-1, 4)
03

Write down the distance formula

The distance formula is given by: \( d = \sqrt{(x2 - x1)^2 + (y2 - y1)^2} \)
04

Plug in the coordinates into the distance formula

We will now substitute the coordinates of points A and B into the distance formula: \( d = \sqrt{(-1 - 3)^2 + (4 - (-2))^2} \)
05

Calculate the distance

Perform the calculations inside the square root: \( d = \sqrt{(-4)^2 + (6)^2} \) \( d = \sqrt{16 + 36} \) Next, add the numbers inside the square root, and finally, calculate the square root: \( d = \sqrt{52} \)
06

Simplify if possible

If possible, simplify the square root. In this case, since 52 can be written as \( 2^2 \times 13 \), the distance can be simplified to: \( d = 2\sqrt{13} \) Now we have found the distance between points (3,-2) and (-1,4): \( d = 2\sqrt{13} \)

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