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 mid - point between 2 points.
$m=(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$
midpoint = ()

Explanation:

1. Identify the two - points:

• From the graph, assume the two points are \((x_1,y_1)=(-4,1)\) and \((x_2,y_2)=(4,0)\).

1. Calculate the distance between the two points:

• Use the distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).
• Substitute \(x_1=-4,y_1 = 1,x_2 = 4,y_2=0\) into the formula:
• First, calculate \((x_2 - x_1)\) and \((y_2 - y_1)\): \(x_2 - x_1=4-(-4)=8\) and \(y_2 - y_1=0 - 1=-1\).
• Then, calculate \((x_2 - x_1)^2+(y_2 - y_1)^2\): \((x_2 - x_1)^2+(y_2 - y_1)^2=8^2+(-1)^2=64 + 1=65\).
• So, \(d=\sqrt{65}\approx 8.06\).

1. Calculate the mid - point between the two points:

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

Step1: Identify points

Assume points \((-4,1)\) and \((4,0)\)

Step2: Calculate distance

\(d=\sqrt{(4 - (-4))^2+(0 - 1)^2}=\sqrt{64 + 1}=\sqrt{65}\approx8.06\)

Step3: Calculate mid - point

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

Answer:

Distance = \(8.06\)
Midpoint = \((0,0.5)\)