Question

hw2.5 euclideancoordinates: problem 6
(1 point)
consider the two points $(-1,8)$ and $(8,-6)$. the distance between them is
the x co - ordinate of the midpoint of the line segment that joins them is
the y co - ordinate of the midpoint of the line segment that joins them is
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Explanation:

Step1: Calculate the distance between two points

Use the distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Let \((x_1,y_1)=(-1,8)\) and \((x_2,y_2)=(8,-6)\).

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Step2: Calculate the \(x\) - coordinate of the mid - point

Use the mid - point formula \(M_x=\frac{x_1 + x_2}{2}\).

$$M_x=\frac{-1+8}{2}=\frac{7}{2}=3.5$$

Step3: Calculate the \(y\) - coordinate of the mid - point

Use the mid - point formula \(M_y=\frac{y_1 + y_2}{2}\).

$$M_y=\frac{8+(-6)}{2}=\frac{8 - 6}{2}=1$$

Answer:

The distance is \(\sqrt{277}\), the \(x\) - coordinate of the mid - point is \(3.5\), and the \(y\) - coordinate of the mid - point is \(1\).