Question

find the length of the segment connecting (-2,4) and (0,-5). provide an answer accurate to the nearest tenth.

Explanation:

Step1: Identify the coordinates

Let \((x_1,y_1)=(-2,4)\) and \((x_2,y_2)=(0, - 5)\)

Step2: Use the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)

Substitute the values: \(d=\sqrt{(0-(-2))^2+(-5 - 4)^2}=\sqrt{(2)^2+(-9)^2}\)

Step3: Calculate the squares

\((2)^2 = 4\) and \((-9)^2=81\), so \(d=\sqrt{4 + 81}=\sqrt{85}\)

Step4: Find the square - root and round

\(\sqrt{85}\approx9.2\)

Answer:

\(9.2\)