Question

You are building a shelf that fits in a corner. In the figure, the entire shelf is △XYZ. Each unit in the coordinate plane represents one inch.

Answer 1

Complete Question: You are building a shelf that fits in a corner in the figure the entire shelf is XYZ each unit in the coordinate plane represents one inch find the area of the shelf.

Answer:

112.5 units²

Explanation:

Area of the shelf = ½*base*height.

The base is the distance between Z(0, 5) and Y(15, 5)

The height is the distance between X(15, 20) and Y(15, 5).

Therefore area of the shelf = ½*ZY*XY

Use the distance formula to find ZY and XY.

Distance between Z(0, 5) and Y(15, 5):

`ZY = √((x_2 - x_1)^2 + (y_2 - y_1)^2)`

Let,

`Z(0, 5) = (x_1, y_1)`

`Y(15, 5) = (x_2, y_2)`

`ZY = √((15 - 0)^2 + (5 - 5)^2)`

`AB = √((15)^2 + (0)^2)`

`AB = √(225 + 0) = √(225)`

`AB = 15`

Distance between X(15, 20) and Y(15, 5):

`XY = √((x_2 - x_1)^2 + (y_2 - y_1)^2)`

Let,

`X(15, 20) = (x_1, y_1)`

`Y(15, 5) = (x_2, y_2)`

`XY = √((15 - 15)^2 + (5 - 20)^2)`

`XY = √((0)^2 + (-15)^2)`

`XY = √(0 + 225) = √(225)`

`XY = 15`

Area of shelf = ½*15*15 = ½*225 = 112.5 units²