The points P(3, –2), Q(10, –2), and R(3, –8) are the vertices of a triangle. What is the approximate length of side RQ?
Question
The points P(3, –2), Q(10, –2), and R(3, –8) are the vertices of a triangle. What is the approximate length of side RQ?
Solution
To find the length of side RQ, we can use the distance formula which is derived from the Pythagorean theorem. The distance between two points (x1, y1) and (x2, y2) in a plane is given by:
d = sqrt[(x2 - x1)² + (y2 - y1)²]
Here, R(3, -8) and Q(10, -2) are the two points. So, x1 = 3, y1 = -8, x2 = 10, and y2 = -2.
Substitute these values into the formula:
d = sqrt[(10 - 3)² + (-2 - (-8))²] d = sqrt[(7)² + (6)²] d = sqrt[49 + 36] d = sqrt[85]
Therefore, the approximate length of side RQ is sqrt[85] or approximately 9.22 units.
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