Put the steps in order to find the distance between these 2 points.

Question

(-2, 1) and (4, 3)
(7 points)
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Step 1
Step 2
Step 3
Step 4
Step 5
Step 6
Step 7

responses
use the Pythagorean theorem for right triangles to determine the diagonal length: 2 has a 2 exponent + 6 has a exponent that's 2 = c has a exponent that's 2
40 = c has an exponent 2
draw a right triangle by dropping a vertical side and a horizontal side.
square root of 40 = square root of c 2 is the exponent
square root of 40 is between square root of 36 and square root of 49, so between 6 and 7 - closer to 6, so about 6.3 units
determine the vertical side (2 units) and horizontal side (6 units) lengths by counting on the grid (be careful of the scale), or using the vertical coordinates (-2, 4).
4 + 36 = c 2 is the exponent

Answer 1

To find the distance between the points (-2, 1) and (4, 3), you can follow these steps in the correct order:

1. Step 1: Draw a right triangle by dropping a vertical side and a horizontal side.

2. Step 2: Determine the vertical side (2 units) and horizontal side (6 units) lengths by counting on the grid (be careful of the scale), or using the vertical coordinates (-2, 4).

3. Step 3: Use the Pythagorean theorem for right triangles to determine the diagonal length: \(2^2 + 6^2 = c^2\).

4. Step 4: \(4 + 36 = c^2\).

5. Step 5: \(40 = c^2\).

6. Step 6: Square root of 40 = square root of \(c^2\) (c is the exponent).

7. Step 7: Square root of 40 is between square root of 36 and square root of 49, so between 6 and 7 - closer to 6, so about 6.3 units.

This sequence provides a systematic approach to finding the distance using the distance formula derived from the Pythagorean theorem.