Question

the graph shows point a and point b.
part a
what is the distance between point a and point b?
○ 2 units
○ 6 units

Explanation:

Step1: Identify coordinates of points

Point $A: (-2, -2)$, Point $B: (2, 7)$

Step2: Apply distance formula

The distance formula is $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$. Substitute $x_1=-2,y_1=-2,x_2=2,y_2=7$:

$$ d=\sqrt{(2-(-2))^2+(7-(-2))^2} $$

Step3: Simplify the expression

First calculate inside the parentheses:

$$ d=\sqrt{(4)^2+(9)^2}=\sqrt{16+81}=\sqrt{97} $$

(Note: If we check the vertical/horizontal difference first: $\Delta x=4$, $\Delta y=9$, so the straight-line distance is $\sqrt{4^2+9^2}$)

Answer:

$\sqrt{97}$ units (approximately 9.85 units)