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Bad White [126]
3 years ago
9

Line segment AB on the coordinate plane stretches from (1,1) to (7,9). Line segment CD stretches from (-2,3) to (2,6). What is t

he ratio AB:CD of the lengths of these line segments
A. 3:2
B 2:1
C 2:3
D 3:1
Mathematics
1 answer:
ValentinkaMS [17]3 years ago
4 0

Answer:

B 2:1

Step-by-step explanation:

Distance between two points:

Suppose that we have two points, (x_1,y_1) and (x_2,y_2). The distance between them is given by:

D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

In this question:

The length of the segments are given by the distance between its endpoints.

Line segment AB on the coordinate plane stretches from (1,1) to (7,9).

So its length is:

\sqrt{(7-1)^2+(9-1)^2} = \sqrt{6^2+8^2} = \sqrt{100} = 10

Line segment CD stretches from (-2,3) to (2,6).

\sqrt{(2-(-2))^2+(6-3)^2} = \sqrt{4^2+3^2} = \sqrt{25} = 5

What is the ratio AB:CD of the lengths of these line segments?

10:5 = 2:1

So the correct answer is given by option B.

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There are \dbinom83 ways of picking 3 of the 8 available positions for a 1. 5 positions remain, but we're filling all of them with 2s, and there's \dbinom55=1 way of doing that.

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