Question

Find the distance between the points (8,
–
2) and (2,10).

Answer 1

To find the distance between two points, we can use the distance formula. The distance formula is derived from the Pythagorean theorem: d = √((x2 - x1)^2 + (y2 - y1)^2)

Let's assign the coordinates of the first point to (x1, y1) and the coordinates of the second point to (x2, y2):

(x1, y1) = (8, -2)
(x2, y2) = (2, 10)

Now let's substitute the values into the distance formula:

d = √((x2 - x1)^2 + (y2 - y1)^2)
= √((2 - 8)^2 + (10 - (-2))^2)
= √((-6)^2 + (10 + 2)^2)
= √(36 + 12^2)
= √(36 + 144)
= √180
≈ 13.42

Therefore, the distance between the points (8, -2) and (2, 10) is approximately 13.42 units.