Question

ashleys house and the public library are plotted on the coordinate plane as shown. what is the distance between ashleys house and the public library to the nearest tenth?
a. 4.7 blocks

Explanation:

Step1: Determine the coordinates

Ashley's house is at \((4,2)\) and the Public Library is at \((10,6)\).

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

Here \(x_1 = 4,y_1 = 2,x_2 = 10,y_2 = 6\).
Substitute into the formula: \(d=\sqrt{(10 - 4)^2+(6 - 2)^2}=\sqrt{6^2 + 4^2}\).

Step3: Calculate the values inside the square - root

\(6^2=36\) and \(4^2 = 16\), so \(d=\sqrt{36+16}=\sqrt{52}\).

Step4: Simplify \(\sqrt{52}\)

\(\sqrt{52}=\sqrt{4\times13}=2\sqrt{13}\approx2\times3.6055 = 7.211\approx7.2\)

Answer:

\(7.2\) blocks