Max is drawing plans for a garden, measured in feet, which is shown below on the coordinate plane. max has two vertices
of the garden at points (-1, 2) and (-1,-2).
at which points should max have the other two vertices in order to make the area of his garden 20 square feet?

The other two vertices are (4 , -2) and (4 , 2) ⇒ 2nd answer

Step-by-step explanation:

* Lets explain how to solve the problem

- All the points on a vertical line have thee same x-coordinates

- In the vertical segment whose endpoints are (x , y1) and (x , y2)

 its length = y2 - y1

- All the points on a horizontal line have thee same y-coordinates

- In the horizontal segment whose endpoints are (x1 , y) and (x2 , y)

 its length = x2 - x1

* Lets solve the problem

- The two vertices of the garden are (-1 , 2) , (-1 , -2)

- The side joining the two vertices is vertical because the points have

  the same x-coordinate

∴ The length of the height = 2 - -2 = 2 + 2 = 4

∴ The length of the height of the garden is 4 feet

∵ The garden shaped a rectangle

∵ The area of the garden is 20 feet²

- The area of the rectangle = base × height

∵ The height = 4 feet

∴ 20 = base × 4 ⇒ divide both sides by 4

∴ Base = 5 feet

∴ The length of the base of the garden is 5 feet

- The adjacent side to the height of the rectangle is horizontal line

∵ The points on the horizontal line have the same y-coordinates

∴ The adjacent vertex to vertex (-1 , 2) has the same y-coordinates 2

∵ The length of the horizontal segment is x2 - x1

∴ 5 = x - (-1)

∴ 5 = x + 1 ⇒ subtract 1 from both sides

∴ x = 4

∴ The adjacent vertex to (-1 , 2) is (4 , 2)

- Lets find the other vertex by the same way

∵ The adjacent vertex to vertex (-1 , -2) has the same y-coordinates -2

∵ x-coordinate of this vertex is the same with x- coordinate of point

 (4 , 2) because these two points formed vertical side

∴ The other vertex is (4 , -2)

∴ The adjacent vertex to (-1 , -2) is (4 , -2)

* The other two vertices are (4 , -2) and (4 , 2)

practice. practice. practice.