Question

Find the length of segment JK with endpoints J(4, 8) and K(-1, -2). Leave the answer as a radical. Simplify if necessary

Answer 1

The length of segment JK is 5
`√(5)` ⇒ C

Explanation:

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

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

Let us use the formula above to solve the question

∵ Jk is a line segment

∵ J = (4, 8) and K = (-1, -2)

∴ x1 = 4 and y1 = 8

∴ x2 = -1 and y2 = -2

→ Substitute them in the formula above

∵ JK =
`\sqrt{(-1-4)^(2)+(-2-8)^(2)}`

∴ JK =
`\sqrt{(-5)^(2)+(-10)^(2)}`

∴ Jk =
`√(25+100)`

∴ Jk =
`√(125)`

→ Simplify the root

∵ 125 = 5 × 5 × 5

∴
`√(125)` = 5
`√(5)`

∴ JK = 5
`√(5)`

∴ The length of segment JK is 5
`√(5)`