Question

Using PT in the Coordinate System

llus
Find the distance between the two points.
(-1,3)
(4,2)
✓ [?]
Enter the number that
goes beneath the
radical symbol.

Answer 1

The distance between the two points is
`√(26)`

Explanation:

The formula of the distance between two points (x1, y1) and (x2, y2) is

d =
`\sqrt{(x2-x1)^(2)+(y2-y1)^(2)}`

∵ The points are (-1, 3) and (4, 2)

∴ x1 = -1 and x2 = 4

∴ y1 = 3 and y2 = 2

→ Substitute them in the formula of the distance above

∵ d =
`\sqrt{(4--1)^(2)+(2-3)^(2)}`

∴ d =
`\sqrt{(4+1)^(2)+(-1)^(2)}`

∴ d =
`\sqrt{(5)^(2)+1}`

∴ d =
`√(25+1)`

∴ d =
`√(26)`

∴ The distance between the two points is
`√(26)`