Question

(4, 7) (7, 3) whats the length between them? if its a square, whats the area?

Answer 1

To find the distance between the two points \((4, 7)\) and \((7, 3)\), we can use the distance formula:

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

Here, \((x_1, y_1) = (4, 7)\) and \((x_2, y_2) = (7, 3)\).

Substituting the coordinates into the formula:

\[
d = \sqrt{(7 - 4)^2 + (3 - 7)^2}
\]
\[
= \sqrt{(3)^2 + (-4)^2}
\]
\[
= \sqrt{9 + 16}
\]
\[
= \sqrt{25}
\]
\[
= 5
\]

So, the length between the two points is \(5\).

To determine if this length represents the side of a square, we can calculate the area of the square using the formula:

\[
\text{Area} = \text{side length}^2
\]

If we take the length of \(5\) as the side length:

\[
\text{Area} = 5^2 = 25
\]

Thus, if related to a square, the area would be \(25\).