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2 years ago

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

Mathematics

1 answer:

Alex777 [14]2 years ago

6 0

Answer:

The length of segment JK is 5 $\sqrt{5}$ ⇒ C

Step-by-step 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 = $\sqrt{25+100}$

∴ Jk = $\sqrt{125}$

→ Simplify the root

∵ 125 = 5 × 5 × 5

∴ $\sqrt{125}$ = 5 $\sqrt{5}$

∴ JK = 5 $\sqrt{5}$

∴ The length of segment JK is 5 $\sqrt{5}$

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