Question

Find the length of the diagonal BD in the quadrilateral ABCD shown in the coordinate plane.

Answer 1

Answer: Choice C)
`√(85) \text{ units}`

Work Shown:

B = (4,3)

D = (-2,-4)

Use the distance formula to get:

`d = √((x_1 - x_2)^2 + (y_1 - y_2)^2)\\\\d = √((4-(-2))^2 + (3-(-4))^2)\\\\d = √((4+2)^2 + (3+4)^2)\\\\d = √((6)^2 + (7)^2)\\\\d = √(36 + 49)\\\\d = √(85)\\\\d \approx 9.21954446\\\\`

You can also use the pythagorean theorem as a slight alternative method.