Question

1. Find the distance between the points A (2,3) and B (7,8)
A) 2√5
B) 5
C) 6.5
D) 5√2

Answer 1

To find the distance between the points \( A(2, 3) \) and \( B(7, 8) \), we use the distance formula:

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

where \( (x_1, y_1) = (2, 3) \) and \( (x_2, y_2) = (7, 8) \).

Substituting the coordinates into the formula:

\[
d = \sqrt{(7 - 2)^2 + (8 - 3)^2}
\]
\[
d = \sqrt{(5)^2 + (5)^2}
\]
\[
d = \sqrt{25 + 25}
\]
\[
d = \sqrt{50}
\]
\[
d = 5\sqrt{2}
\]

Thus, the distance between points A and B is \( 5\sqrt{2} \).

The correct answer is **D) 5√2**.