Question

1. determine the distance between the points (2, 6) and (-1, -3), using the distance formula.

√85
10
9
√90

Explanation:

Step1: Identify the coordinates

Let $(x_1,y_1)=(2,6)$ and $(x_2,y_2)=(-1,-3)$.

Step2: Apply the distance formula

The distance formula is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Substitute the values: $d=\sqrt{(-1 - 2)^2+(-3 - 6)^2}$.

Step3: Calculate the differences

$-1-2=-3$ and $-3 - 6=-9$. So $d=\sqrt{(-3)^2+(-9)^2}$.

Step4: Square the differences

$(-3)^2 = 9$ and $(-9)^2=81$. Then $d=\sqrt{9 + 81}$.

Step5: Add the results

$9+81 = 90$. So $d=\sqrt{90}$.

Answer:

$\sqrt{90}$