Question

The height of XYZ is the distance from the point Y to XZ find the area of the triangle round your answer to the nearest 10th if necessary HELPPP PLEASE

Answer 1

Area of ΔXYZ = 10 square units

Explanation:

Area of the triangle XYZ =
`(1)/(2)(\text{Height})(\text{Base})`

Height of the triangle = AY

Base of the triangle = XZ

To get the length of any segment we will use the formula,

d =
`√((y_2-y_1)^2+(x_2-x_1)^2))`

Here
`(x_1,y_1)` and
`(x_2,y_2)` are the endpoints of the segment.

Length of AY = Distance between (-1, 4) and (3, 6)

=
`√((6-4)^2+(3+1)^2)`

=
`√(20)`

Length of XZ =
`√((6-2)^2+(-2-0)^2)`

=
`√(20)`

Area of ΔXYZ =
`(1)/(2)(√(20))(√(20))`

= 10 square units