(4, 3)

Question

(2,1)
Put the steps in order to find the distance between these 2 points.
Step 1

Step 2

Step 3

Step 4

Step 5

Step 6

Step 7

Use the Pythagorean Theorem for right triangles to determine the diagonal length: 2 ^ 2 + 6 ^ 2 = c ^ 2

40 = c ^ 2

Draw a right triangle by dropping a vertical side and a horizontal side.

sqrt(40) = sqrt(c ^ 2)

sqrt(40) between sqrt(36) and sqrt(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 (3 to 1) and horizontal coordinates (-2 to 4).

=4 + 36 = c ^ 2

Answer 1

Step 1: Determine the vertical side length by subtracting the y-coordinates: 3 - 1 = 2 units.

Step 2: Determine the horizontal side length by subtracting the x-coordinates: 4 - (-2) = 6 units.

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

Step 4: Simplify the equation: 4 + 36 = c^2.

Step 5: Add the two values: 40 = c^2.

Step 6: Take the square root to solve for c: sqrt(40) = c.

Step 7: Approximate the distance: sqrt(40) is between sqrt(36) and sqrt(49), so it is closer to 6 and estimated to be about 6.3 units.