Question

An architect maps two buildings, which are located on a piece of land, onto a coordinate plane. He wants to build a wall at the diagonal AC to divide the piece of land into two parts. What will be the length of the wall? A. 65–√ units B. 6 units C. 237−−√ units D. 2 units

Answer 1

`6√(5) units`

Explanation:

The length of the wall = diagonal AC = distance between point A (-6, -2) and point C (6, 4).

Distance formula between two points on a graph (d) =
`√((x_2 - x_1)^2 + (y_2 - y_1)^2)`

Where,

`A(-6, -2) = (x_1, y_1)`

`C(6, 4) = (x_2, y_2)`

`d = √((6 - (-6))^2 + (4 -(-2))^2)`

`d = √((6 + 6)^2 + (4 + 2)^2)`

`d = √((12)^2 + (6)^2)`

`d = √(144 + 36)`

`d = √(180)`

`d = √(36*5)`

`d = 6√(5)`

The length of the wall =
`6√(5) units`