Question

1. find the distance between the points (2,3) and (7,7).
2. find the distance between the points (-4,5) and (-1,1). *

your answer

1. find the midpoint between the points (-2,3) and (-7,-7). *

(-4.5,-2)

1. the midpoint of line eg is at f(1,10). if point e is located at (6,-2), where would point g be?

-4, 22

1. find the distance between the points (-4,-3) and (-1,1). *

Explanation:

1.

Step1: Identify distance - formula

The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Here \(x_1 = 2,y_1 = 3,x_2=7,y_2 = 7\).
\[d=\sqrt{(7 - 2)^2+(7 - 3)^2}\]

Step2: Calculate differences

\(7−2 = 5\) and \(7 - 3=4\). So \(d=\sqrt{5^2+4^2}\).
\[d=\sqrt{25 + 16}\]

Step3: Simplify the square - root

\(d=\sqrt{41}\approx6.4\)

Step1: Apply distance formula

Using \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\), with \(x_1=-4,y_1 = 5,x_2=-1,y_2 = 1\).
\[d=\sqrt{(-1+4)^2+(1 - 5)^2}\]

Step2: Calculate differences

\(-1 + 4=3\) and \(1-5=-4\). So \(d=\sqrt{3^2+(-4)^2}\).
\[d=\sqrt{9 + 16}\]

Step3: Simplify the square - root

\(d=\sqrt{25}=5\)

Step1: Recall mid - point formula

The mid - point formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \((\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})\). Here \(x_1=-2,y_1 = 3,x_2=-7,y_2=-7\).
\[x=\frac{-2-7}{2}=\frac{-9}{2}=-4.5,y=\frac{3-7}{2}=\frac{-4}{2}=-2\]

Answer:

\(\sqrt{41}\approx6.4\)

2.