Question

13 fill in the blank 4 points given the points, a(3, 1) and b(9, 7), find the midpoint and the distance, as a square root and as a decimal rounded to the nearest tenth. the slope is type your answer... the midpoint is type your answer... type your answer... the distance of the segment is the square root of type your answer... and, in decimal form, type your answer... previous

Explanation:

Step1: Calculate the slope

The slope formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Here $x_1 = 3,y_1=1,x_2 = 9,y_2 = 7$. So $m=\frac{7 - 1}{9 - 3}=\frac{6}{6}=1$.

Step2: Calculate the mid - point

The mid - point formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Substitute $x_1 = 3,y_1=1,x_2 = 9,y_2 = 7$ into the formula, we get $(\frac{3+9}{2},\frac{1 + 7}{2})=(6,4)$.

Step3: Calculate the distance

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Substitute $x_1 = 3,y_1=1,x_2 = 9,y_2 = 7$ into the formula: $d=\sqrt{(9 - 3)^2+(7 - 1)^2}=\sqrt{6^2+6^2}=\sqrt{36 + 36}=\sqrt{72}$. In decimal form, $\sqrt{72}\approx8.5$.

Answer:

The slope is 1.
The midpoint is (6,4).
The distance of the segment is the square root of 72 and, in decimal form, 8.5.