Westonci.ca is the Q&A platform that connects you with experts who provide accurate and detailed answers. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.

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.