Answered

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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 the ratio AB:CD of the lengths of these line segments
A. 3:2
B 2:1
C 2:3
D 3:1

Sagot :

Answer:

B 2:1

Step-by-step explanation:

Distance between two points:

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

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

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:

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

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

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

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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