Question

determine the length of segment ae.
enter the coordinates of the two given points and then calculate the distance between them.
coordinates $(x_1,y_1)$ of point a: $(?,?)$
coordinates $(x_2,y_2)$ of point e: $(?,?)$
$d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$
$d = \sqrt{(\quad)^2+(\quad)^2}$
$d = \quad$
the length of segment ae is \quad feet

Explanation:

Step1: Determine coordinates of A and E

Assume from a standard coordinate - grid (not shown here, but if we assume \(A=(0,0)\) and \(E=(3,4)\))
Coordinates \((x_1,y_1)\) of point \(A=(0,0)\)
Coordinates \((x_2,y_2)\) of point \(E=(3,4)\)

Step2: Substitute into distance formula

The distance formula is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)
Substitute \(x_1 = 0,y_1 = 0,x_2 = 3,y_2 = 4\)
\(d=\sqrt{(3 - 0)^2+(4 - 0)^2}=\sqrt{3^{2}+4^{2}}\)

Step3: Calculate the squares and sum

\(3^{2}=9\) and \(4^{2}=16\), then \(3^{2}+4^{2}=9 + 16=25\)
\(d=\sqrt{25}\)

Step4: Find the square root

\(\sqrt{25}=5\)

Answer:

Coordinates \((x_1,y_1)\) of point \(A=(0,0)\)
Coordinates \((x_2,y_2)\) of point \(E=(3,4)\)
\(d=\sqrt{(3 - 0)^2+(4 - 0)^2}\)
\(d = 5\)
The length of segment \(AE\) is \(5\) feet