Question

1. Find the distance between the two points:

(5,3) and (-2,8)
O √5
O 4√7
O 2√3
O√74

Answer 1

`\huge{ \boxed{ √(74) }}`

Explanation:

The distance between the two points can be found by using the formula;

`|d| = \sqrt{(x _(1) - x _(2))^(2) + {(y_(1) - y _(2))}^(2) }`

where (x1, y1) and (x2, y2) are the points

From the question the points are (5,3) and (-2,8).

`\therefore \: |d| = \sqrt{ ({5 - - 2})^(2) + ({3 - 8})^(2) } \\ \implies \sqrt{ ({5 + 2})^(2) + ( { - 5})^(2) } \\ \implies \sqrt{ {7}^(2) + ( { - 5})^(2) } \\ \implies √(49 + 25) \\ = √(74) \\`

We have the final answer as:

`\large{ √(74) }`