Question

find the distance between the coordinates given. *
11 d(5,6), e(-3,8)
10
find the distance between the coordinates given. *
12 r(4, -9), s(-7,-2)
your answer
this is a required question

Explanation:

Problem 11: Distance between \( D(5,6) \) and \( E(-3,8) \)

Step1: Recall 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, \( x_1 = 5,y_1 = 6,x_2=- 3,y_2 = 8 \).

Step2: Substitute values into formula

Substitute the values: \( d=\sqrt{(-3 - 5)^2+(8 - 6)^2}=\sqrt{(-8)^2+(2)^2}=\sqrt{64 + 4}=\sqrt{68}=2\sqrt{17}\approx8.25 \) (if decimal is needed) or keep it as \( 2\sqrt{17} \)

Problem 12: Distance between \( R(4,-9) \) and \( S(-7,-2) \)

Step1: Recall 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, \( x_1 = 4,y_1=-9,x_2 = - 7,y_2=-2 \)

Step2: Substitute values into formula

Substitute the values: \( d=\sqrt{(-7 - 4)^2+(-2-(-9))^2}=\sqrt{(-11)^2+(7)^2}=\sqrt{121 + 49}=\sqrt{170}\approx13.04 \) (if decimal is needed) or keep it as \( \sqrt{170} \)

Answer:

(Problem 11): \( 2\sqrt{17} \) (or approximately \( 8.25 \))