Question

1 calculate the distance between the following two points.
a(3,7) b(6,11)
my calculations grid

2 calculate the distance between the following two points:
a(-7,3) b(2,-1)
my calculations grid

3 calculate the distance between the following two points.
a(-6,2) b(-3,2)
my calculations grid

4 find the perimeter of the triangle on the graph below.
graph with points a(-1,-2), b(1,4), c(5,-1)
my calculations grid

Explanation:

Problem 1: Distance between \( A(3,7) \) and \( B(6,11) \)

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, \( x_1 = 3,y_1 = 7,x_2 = 6,y_2 = 11 \).

Step2: Substitute values into formula

\( d=\sqrt{(6 - 3)^2+(11 - 7)^2}=\sqrt{3^2 + 4^2}=\sqrt{9 + 16}=\sqrt{25} = 5 \)

Step1: Use distance formula

For points \((x_1,y_1)=(-7,3)\) and \((x_2,y_2)=(2,-1)\), distance \( d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2} \)

Step2: Substitute and calculate

\( d=\sqrt{(2-(-7))^2+(-1 - 3)^2}=\sqrt{(9)^2+(-4)^2}=\sqrt{81 + 16}=\sqrt{97}\approx9.85 \) (if we want decimal approximation) or keep it as \( \sqrt{97} \)

Step1: Identify coordinates

Here, \( y_1 = y_2=2 \), so the distance is horizontal. The formula for horizontal distance is \( |x_2 - x_1| \)

Step2: Calculate

\( d=|-3-(-6)|=|-3 + 6|=|3| = 3 \)

Answer:

5

Problem 2: Distance between \( A(-7,3) \) and \( B(2,-1) \)