Question

b. what is the distance between (2,9) and (1,5)?

Explanation:

Step1: Recall distance formula

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

Step2: Identify coordinates

Here, \( x_1 = 2,y_1 = 9,x_2 = 1,y_2 = 5 \).

Step3: Substitute into formula

\( d=\sqrt{(1 - 2)^2+(5 - 9)^2}=\sqrt{(- 1)^2+(-4)^2}=\sqrt{1 + 16}=\sqrt{17}\approx4.123 \)

Answer:

The distance between \((2,9)\) and \((1,5)\) is \(\sqrt{17}\) (or approximately \(4.12\)).