Question

Daniella is drawing plans for a garden, measured in feet, which is shown below on the coordinate plane. Daniella has two vertices of the garden at points (-3,-1)

Answer 1

`(2,-1)` and
`(9,-1)`

Explanation:

Given

`(x_1,y_1) = (-3,-1)`

`(x_2,y_2) = (4,-1)`

`Area = 35ft^2`

Required

The other two points

First, calculate the distance between the given points using:

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

`d = √((-3 - 4)^2 + (-1- -1)^2)`

`d = √((-7)^2 + (0)^2)`

`d = √(49 + 0)`

`d = √(49)`

`d = 7`

Calculate the length of the other part using:

`Length = (Area)/(d)`

`Length = (35)/(7)`

`Length = 5`

This means that the other points is 5 units (up or down) away from the given points

Assume the new points are up, the new dimension is:

`(x_3,y_3) = (-3+5,-1)`

`(x_3,y_3) = (2,-1)`

`(x_3,y_3) = (4+5,-1)`

`(x_3,y_3) = (9,-1)`