Find the distance between the two points in simplest radical form.left bracket, 8, comma, minus, 1, right bracket, and , left bracket, 2, comma, minus, 9, right bracket(8,−1) and (2,−9)
Question
Find the distance between the two points in simplest radical form.left bracket, 8, comma, minus, 1, right bracket, and , left bracket, 2, comma, minus, 9, right bracket(8,−1) and (2,−9)
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 formula is:
d = sqrt[(x2 - x1)² + (y2 - y1)²]
Here, the two points are (8, -1) and (2, -9). So, x1 = 8, y1 = -1, x2 = 2, and y2 = -9.
Substitute these values into the distance formula:
d = sqrt[(2 - 8)² + (-9 - (-1))²] d = sqrt[(-6)² + (-8)²] d = sqrt[36 + 64] d = sqrt[100]
The square root of 100 is 10. So, the distance between the points (8, -1) and (2, -9) is 10 units.
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