Final answer:
The distance between the points (5,1) and (-3,-3) is found using the distance formula, yielding a result of 4√5 units in simplest radical form.
Step-by-step explanation:
To find the distance between two points in a coordinate plane, you can use the distance formula, which is derived from the Pythagorean theorem. The distance formula is:
d = √((x2 - x1)² + (y2 - y1)²)
For the points (5,1) and (-3,-3), let's substitute the coordinates into the formula:
d = √((-3 - 5)² + (-3 - 1)²)
This simplifies to:
d = √((-8)² + (-4)²)
d = √(64 + 16)
d = √80
Since 80 = 16 * 5 and 16 is a perfect square, we can simplify √80:
d = √(16 * 5)
d = 4√5
Therefore, the distance between the points (5,1) and (-3,-3) in simplest radical form is 4√5 units.