Answered

A city map is placed on a coordinate grid. The post office is located at the point

P ( 5, 35) , the library is located at the point L (15, 10) , and the fire station is

located at the point F  (9, 25) . What is the ratio of the length of PF to the length of

LF ?

A 2 : 3

B 3 : 2

C 2 : 5

D 3 : 5

Verified Answer :

naǫ

The distance between two points:
\(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)
(x₁,y₁), (x₂,y₂) - the coordinates of the points

\(P(5,35) \\ L(15,10) \\ F(9,25) \\ \\ \overline{PF} = \sqrt{(9-5)^2+(25-35)^2}=\sqrt{4^2+(-10)^2}=\sqrt{16+100}= \\ =\sqrt{116}=\sqrt{4 \times 29}=2\sqrt{29} \\ \\ \overline{LF}=\sqrt{(9-15)^2+(25-10)^2}=\sqrt{(-6)^2+15^2}=\sqrt{36+225}= \\ =\sqrt{261}=\sqrt{9 \times 29}=3\sqrt{29} \\ \\ \frac{\overline{PF}}{\overline{LF}}=\frac{2\sqrt{29}}{3\sqrt{29}}=\frac{2}{3}=2:3\)

The answer is A.

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