Question

If the blueprint is drawn on the coordinate plane with vertices (1, 5) and (11, 15) for the corners labeled with red stars, would that be an accurate representation of the length of the diagonal of the square C? Show your work and explain your reasoning. (4 points—2 points for finding the length of the diagonal; 2 points for explanation)

Answer 1

50^2

Step-by-step explanation: edge thingy :]

Answer 2

`50√(2)\: feet`

Explanation:

In the coordinate plane, two of the vertices of Square C are (1, 5) and (11, 15).

The length of the diagonal of Square C is the straight line joining the two points.

Using the distance formula in coordinate geometry:

`Distance=√((x_2-x_1)^2+(y_2-y_1)^2) \\(x_1,y_1)=(1, 5) ,(x_2,y_2)= (11, 15)\\Distance=√((11-1)^2+(15-5)^2) =√(10^2+10^2) =√(200)\\Distance=10√(2)`

On the graph,

1 square Unit =25 Square Feet

1 Unit =5 feet.

Therefore:

Length of the diagonal of square C

`=5*10√(2)\\=50√(2)\: feet`