Question

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

Answer 1

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.