Question

given:
c(-5, -4), d(-2, -7)
find: cd

given:
l(2, -2), m(8, -1)
find: lm

Explanation:

First Sub - Question: Find \( CD \) with \( C(-5,-4) \) and \( D(-2,-7) \)

Step1: Recall the 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, \( x_1=-5,y_1 = - 4,x_2=-2,y_2=-7 \).

Step2: Substitute values into the formula

First, calculate \( x_2 - x_1=-2-(-5)=-2 + 5 = 3 \) and \( y_2 - y_1=-7-(-4)=-7 + 4=-3 \).
Then, \( CD=\sqrt{(3)^2+(-3)^2}=\sqrt{9 + 9}=\sqrt{18}=\sqrt{9\times2}=3\sqrt{2} \)

Second Sub - Question: Find \( LM \) with \( L(2,-2) \) and \( M(8,-1) \)

Step1: Recall the 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, \( x_1 = 2,y_1=-2,x_2 = 8,y_2=-1 \).

Step2: Substitute values into the formula

First, calculate \( x_2 - x_1=8 - 2=6 \) and \( y_2 - y_1=-1-(-2)=-1 + 2 = 1 \).
Then, \( LM=\sqrt{(6)^2+(1)^2}=\sqrt{36 + 1}=\sqrt{37} \)

Answer:

For \( CD \): \( 3\sqrt{2} \)
For \( LM \): \( \sqrt{37} \)