Question 6

Calculate the distance between the points $M=(0,-1)$ and $Q=(-7,5)$ in the coordinate plane.
Round your answer to the nearest hundredth.

Answer

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Answer

$\boxed{d \approx 9.22}$

Steps

Step 1 ：$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

Step 2 ：Substitute $x_1 = 0$, $y_1 = -1$, $x_2 = -7$, and $y_2 = 5$ into the formula

Step 3 ：$d = \sqrt{(-7 - 0)^2 + (5 - (-1))^2}$

Step 4 ：Simplify inside the parentheses: $d = \sqrt{(-7)^2 + (6)^2}$

Step 5 ：Square the numbers: $d = \sqrt{49 + 36}$

Step 6 ：Add the numbers: $d = \sqrt{85}$

Step 7 ：The square root of 85 is approximately 9.22 when rounded to the nearest hundredth

Step 8 ：$\boxed{d \approx 9.22}$