Question

1. use the pythagorean theorem to find the distance between (6, -1) and (-9, 1). round to the nearest tenth

Explanation:

Step1: Find the horizontal distance

The horizontal distance $x$ between the points $(6,-1)$ and $(-9,1)$ is the absolute - value of the difference in $x$ - coordinates. Let $(x_1,y_1)=(6,-1)$ and $(x_2,y_2)=(-9,1)$. Then $x=\vert x_2 - x_1\vert=\vert-9 - 6\vert=\vert-15\vert = 15$.

Step2: Find the vertical distance

The vertical distance $y$ between the points is the absolute - value of the difference in $y$ - coordinates. So $y=\vert y_2 - y_1\vert=\vert1-(-1)\vert=\vert1 + 1\vert = 2$.

Step3: Apply the Pythagorean Theorem

The distance $d$ between two points is given by the Pythagorean Theorem $d=\sqrt{x^{2}+y^{2}}$. Substitute $x = 15$ and $y = 2$ into the formula: $d=\sqrt{15^{2}+2^{2}}=\sqrt{225 + 4}=\sqrt{229}\approx15.1$.

Answer:

$15.1$