Question

09/03 - segment bisector practice l (updated)
finding the distance between two points.
distance formula
$d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$
distance = (round to nearest hundredth)
finding the midpoint between 2 points.
$m = (\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$
midpoint = ( )

Explanation:

1. First, assume the two - points from the graph:

• Let the first point be \((x_1,y_1)=(-1,0)\) and the second point be \((x_2,y_2)=(2, - 4)\).

1. Calculate the distance between the two points using the distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\):

• Substitute the values of \(x_1,x_2,y_1,y_2\) into the formula:
• \(x_2 - x_1=2-(-1)=3\), \(y_2 - y_1=-4 - 0=-4\).
• Then \(d=\sqrt{(3)^2+(-4)^2}=\sqrt{9 + 16}=\sqrt{25}=5.00\).

1. Calculate the mid - point between the two points using the mid - point formula \(M=(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})\):

• Substitute \(x_1=-1,x_2 = 2,y_1 = 0,y_2=-4\) into the formula.
• \(\frac{x_1 + x_2}{2}=\frac{-1+2}{2}=\frac{1}{2}=0.5\).
• \(\frac{y_1 + y_2}{2}=\frac{0+( - 4)}{2}=\frac{-4}{2}=-2\).
• So the mid - point \(M=(0.5,-2)\).

Step1: Identify points

\((x_1,y_1)=(-1,0),(x_2,y_2)=(2,-4)\)

Step2: Calculate distance

\(d=\sqrt{(2 - (-1))^2+(-4 - 0)^2}=\sqrt{3^2+( - 4)^2}=\sqrt{9 + 16}=5.00\)

Step3: Calculate mid - point

\(M=(\frac{-1 + 2}{2},\frac{0+( - 4)}{2})=(0.5,-2)\)

Answer:

Distance = \(5.00\)
Midpoint = \((0.5,-2)\)