Question

Use the distance formula to find the length of the diagonal of the square whose vertices are (0,0), (0, 5), (5, 5), and (5,0).

Answer 1

length of the diagonal of the given vertices is 5√2 units

Explanation:

Data provided:

The coordinates of the square as:

(0,0), (0, 5), (5, 5), and (5,0)

on plotting the above points on the graph we, get the square shown in the graph attached

since, in a square all the diagonals are equal, therefore,

we length of diagonal = distance between the coordinates ( 0, 0) and ( 5, 5)

Now,

The distance between the two points whose coordinates is given is calculated using the formula

distance =
`√((x_2-x_1)^2+(y_2-y_1)^2)`

on substituting the respective values, we get

distance =
`√((0-5)^2+(0-5)^2)`

or

distance =
`√(25+25)`

or

distance = √50

or

distance = 5√2 units

Hence,

The length of the diagonal of the given vertices is 5√2 units