Find the distance between the two points in simplest radical form.left bracket, 8, comma, 6, right bracket, and , left bracket, 3, comma, minus, 6, right bracket(8,6) and (3,−6)
Question
Find the distance between the two points in simplest radical form.left bracket, 8, comma, 6, right bracket, and , left bracket, 3, comma, minus, 6, right bracket(8,6) and (3,−6)
Solution
To find the distance between two points (x1, y1) and (x2, y2) in a plane, we use the distance formula which is derived from the Pythagorean theorem. The distance d is given by:
d = sqrt[(x2 - x1)² + (y2 - y1)²]
Here, the two points are (8, 6) and (3, -6). So, x1 = 8, y1 = 6, x2 = 3, and y2 = -6.
Substitute these values into the formula:
d = sqrt[(3 - 8)² + (-6 - 6)²] d = sqrt[(-5)² + (-12)²] d = sqrt[25 + 144] d = sqrt[169]
The square root of 169 is 13. So, the distance between the points (8, 6) and (3, -6) is 13 units.
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