Question

The height of AXYZ is the

distance from point Y to XZ
Find the area of the
triangle. Round your answer
to the nearest tenth, if
necessary. y(4,5) a(2,1) x(0,2) z(4,0)
pls help quick:(

Answer 1

areas of AXYZ=10 square units1

Answer 2

10 units squared

Explanation:

Area of a triangle = 1/2 × base × height

Use the distance between two points formula to find the measure of the height and base of ΔXYZ.

Distance between two points

`d=√((x_2-x_1)^2+(y_2-y_1)^2)`

`\textsf{where }(x_1,y_1) \textsf{ and }(x_2,y_2)\:\textsf{are the two points}`

Height of Triangle

Define the points:

• 
  `\textsf{Let }(x_1,y_1)=(2,1)`
• 
  `\textsf{Let }(x_2,y_2)=(4,5)`

Substitute the points into the distance formula to find the height of the triangle:

`\begin{aligned}\implies \sf height & =√((4-2)^2+(5-1)^2)\\& = √(2^2+4^2)\\& = √(20)\end{aligned}`

Base of Triangle

Define the points:

• 
  `\textsf{Let }(x_1,y_1)=(0,2)`
• 
  `\textsf{Let }(x_2,y_2)=(4,0)`

Substitute the points into the distance formula to find the height of the triangle:

`\begin{aligned}\implies \sf base & =√((4-0)^2+(0-2)^2)\\& = √(4^2+(-2)^2)\\& = √(20)\end{aligned}`

Area of Triangle

`\begin{aligned}\implies \sf Area & = (1)/(2) * \sf base * height\\& = (1)/(2)√(20)√(20)\\& = (1)/(2)(20)\\& = 10 \sf \:\:units^2 \end{aligned}`