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Find the magnitude of the vector PQ→ when P = (-2, 6) and Q = (7, 9). Round to the nearest hundredth.

A) 3.16
B) 6.08
C) 7.62
D) 9.22

1 Answer

2 votes

Final answer:

Using the distance formula, the magnitude of vector PQ→ with points P = (-2, 6) and Q = (7, 9) is calculated to be approximately 9.49, which doesn't match the provided options.

Step-by-step explanation:

To find the magnitude of the vector PQ→ when P = (-2, 6) and Q = (7, 9), we use the distance formula, which is derived from the Pythagorean theorem. The distance formula for two points P(x1, y1) and Q(x2, y2) in a Cartesian coordinate system is:

\(|PQ| = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}\)

Plugging in P = (-2, 6) and Q = (7, 9), we get:

\(|PQ| = \sqrt{(7 - (-2))^2 + (9 - 6)^2} = \sqrt{9^2 + 3^2} = \sqrt{81 + 9} = \sqrt{90}\)

The magnitude of vector PQ→ is therefore:

\(|PQ| = \sqrt{90} \approx 9.49\)

This result is not represented in the given options, which means there might have been a misunderstanding of the question, or a miscalculation, as the correct rounded value, to the nearest hundredth, of the magnitude is 9.49, which is not present in the options.

User Lalit Bhudiya
by
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