Question

Use a coordinate grid to plot the points (—2, 3) and (4, 5) then plot two more points so that all four points form vértices of a rectangle with a horizontal length. Next, find the length of each side. Write an absolute value expression to show how you calculated each length.

Answer 1

The answer to your question is below

Explanation:

See the picture below

Data

A (-2, 3)

B (4, 5)

I plotted the points C (4, 3) and D (-2, 5)

Distance

dAC =
`\sqrt{(4 + 2)^(2)+ (3-3)^(2)}`

=
`\sqrt{(6)^(2)}`

= 6

dBD =
`\sqrt{(4 + 2)^(2)+ (5 - 5)^(2)}`

=
`√(36)`

= 6

dAD =
`\sqrt{(-2 + 2)^(2) + (3 - 5)^(2)}`

=
`\sqrt{(-2)^(2)}`

= 2

dBC =
`\sqrt{(4 - 4)^(2) + (5 - 3)^(2)}`

dBC =
`\sqrt{(2)^(2)}`

dBC = 2

Total distance = dAC + dBD + dAD + dBC

Total distance = 6 + 6 + 2 + 2

= 16

I calculate the length of each side and then I sun them up.