Question

2.2
score: 0/23 answered: 0/23
question 1
find the distance between the pair of points and the midpoint of the line segment joining them.
(5,5),(9,8)
distance:
midpoint: ( )
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Explanation:

Step1: Recall distance formula

The distance $d$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here $x_1 = 5,y_1 = 5,x_2=9,y_2 = 8$.
$d=\sqrt{(9 - 5)^2+(8 - 5)^2}$

Step2: Calculate the values inside the square - root

$(9 - 5)^2=4^2 = 16$ and $(8 - 5)^2=3^2 = 9$. Then $d=\sqrt{16 + 9}=\sqrt{25}=5$.

Step3: Recall mid - point formula

The mid - point $M$ of the line segment joining $(x_1,y_1)$ and $(x_2,y_2)$ is $M=(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$.
$M=(\frac{5 + 9}{2},\frac{5+8}{2})$

Step4: Calculate the mid - point coordinates

$\frac{5 + 9}{2}=\frac{14}{2}=7$ and $\frac{5 + 8}{2}=\frac{13}{2}=6.5$. So $M=(7,6.5)$

Answer:

Distance: 5
Midpoint: (7, 6.5)