Question

A and B are two points on square ABCD with coordinates A(1,3) and B(5,3). What are the lengths of the diagonals AC and BD? Round your answer to the nearest tenths place.

Answer 1

Answer:

$AC = BD = 5.7$

Step-by-step explanation:

Given

$A = (1,3)$

$B = (5,3)$

Required

The length of the diagonals

First, calculate the length of AB using:

$d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}$

So, we have:

$AB = \sqrt{(1 - 5)^2 + (3 - 3)^2}$

$AB = \sqrt{(-4)^2 + 0^2}$

$AB = \sqrt{16}$

$AB = 4$

The diagonal of a square is calculated using:

$Diagonal = x\sqrt{2$

Where x is the length of each side.

So:

$AC = BD = AB\sqrt{2}$

$AC = BD = 4\sqrt{2}$

$AC = BD = 5.7$ -- approximated