Question

11 10 9 8 7 6 5 4 3 2 1 -1.5 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 10.82 7.21 3.61 z(-4,0) e(5,6) d = \sqrt{( )^{2}+( )^{2}} d =

Explanation:

Step1: Substitute coordinates into distance formula

The distance formula is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Let \(Z(-4,0)\) be \((x_1,y_1)\) and \(E(5,6)\) be \((x_2,y_2)\). Then \(x_2 - x_1=5-(-4)=9\) and \(y_2 - y_1 = 6 - 0=6\). So the formula becomes \(d=\sqrt{(9)^2+(6)^2}\).

Step2: Calculate the squares

\(9^2 = 81\) and \(6^2=36\). Then \(d=\sqrt{81 + 36}\).

Step3: Sum and take square - root

\(81+36 = 117\), and \(d=\sqrt{117}\approx10.82\) (using a calculator, \(\sqrt{117}=\sqrt{9\times13}=3\sqrt{13}\approx3\times3.606 = 10.82\)).

Answer:

\(d=\sqrt{(9)^2+(6)^2}\), \(d = 10.82\)