Question

Which expression can be used to determine the length of segment ZY?

On a coordinate plane, triangle X Y Z has points (3, 1), (3, 4), (negative 5, 1).

Answer 1

The length of segment ZY is of
`√(73)` units.

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 = √((x_2-x_1)^2+(y_2-y_1)^2)`

In this question:

Point Z has coordinates (-5,1)

Pount Y has coordinates (3,4).

The length of segment ZY is the distance between points Z and Y. Thus

`D = √((x_2-x_1)^2+(y_2-y_1)^2)`

`D = √((-5-3)^2+(1-4)^2)`

`D = √(8^2+3^2)`

`D = √(73)`

The length of segment ZY is of
`√(73)` units.