Question

What is the approximate length of midsegment MN? What is the approximate length of AB?

A) 1.4; 2.8
B) 2.1; 4.2
C) 2.5; 3.0
D) 2.8; 1.4

Answer 1

A) 1.4; 2.8

Explanation:

We have been given an image of a triangle on coordinate plane and we are asked to find the length of mid-segment MN and segment AB.

First of all, we will find the length of MN using distance formula.

`D=√((x_2-x_1)^2+(y_2-y_1)^2)`

`D_(MN)=√((5-4)^2+(2-1)^2)`

`D_(MN)=√((1)^2+(1)^2)`

`D_(MN)=√(1+1)`

`D_(MN)=√(2)`

`D_(MN)=1.41421356\aaprox 1.4`

Therefore, the length of MN is approximately 1.4 units.

We know that length of mid-segment connecting two sides of a triangle is half the length of third side of the triangle.

To find the length of AB, we will multiply length of mid-segment MN by 2.

`\text{Length of AB}=1.41421356* 2`

`\text{Length of AB}=2.8284\approx 2.8`

Therefore, the length of AB is approximately 2.8 units and option A is the correct choice.