Question

hw2.5 euclideancoordinates: problem 7
(1 point)
consider the two points (5, -2) and (8, 9). 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 \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).
Here \(x_1 = 5,y_1=-2,x_2 = 8,y_2 = 9\).
\(d=\sqrt{(8 - 5)^2+(9-(-2))^2}=\sqrt{3^2+11^2}=\sqrt{9 + 121}=\sqrt{130}\)

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

Use the mid - point formula for \(x\) - coordinate \(M_x=\frac{x_1+x_2}{2}\).
\(M_x=\frac{5 + 8}{2}=\frac{13}{2}=6.5\)

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

Use the mid - point formula for \(y\) - coordinate \(M_y=\frac{y_1+y_2}{2}\).
\(M_y=\frac{-2 + 9}{2}=\frac{7}{2}=3.5\)

Answer:

The distance is \(\sqrt{130}\), the \(x\) - coordinate of the mid - point is \(6.5\), and the \(y\) - coordinate of the mid - point is \(3.5\)