Question

triangles unit test
apply the pythagorean theorem to find the length between the two points. round your answer to the nearest hundredth.
(1 point)

Explanation:

Step1: Find the differences in coordinates

Let the two points be \((x_1,y_1)=(0,0)\) and \((x_2,y_2)=(3,2)\).
The difference in \(x\) - coordinates: \(\Delta x=x_2 - x_1=3 - 0 = 3\).
The difference in \(y\) - coordinates: \(\Delta y=y_2 - y_1=2 - 0 = 2\).

Step2: Apply the Pythagorean theorem

The distance \(d\) between two points \((x_1,y_1)\) and \((x_2,y_2)\) is given by \(d=\sqrt{(\Delta x)^2+(\Delta y)^2}\) (derived from the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(a = \Delta x\), \(b=\Delta y\), and \(c = d\)).
Substitute \(\Delta x = 3\) and \(\Delta y=2\) into the formula: \(d=\sqrt{3^{2}+2^{2}}=\sqrt{9 + 4}=\sqrt{13}\).

Step3: Calculate the value

\(\sqrt{13}\approx3.61\) (using a calculator, \(\sqrt{13}\approx3.60555\), and rounding to the nearest hundredth).

Answer:

\(3.61\)