Question

find the length of line ab in the followi diagram using the distance formula: b(3,10) a(-9,-4)

Explanation:

Step1: Identify coordinates

Let \(A(x_1,y_1)=(-9,-4)\) and \(B(x_2,y_2)=(3,10)\)

Step2: Apply distance formula

The distance formula is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)
Substitute values: \(d=\sqrt{(3-(-9))^2+(10 - (-4))^2}\)
Simplify inside the square root:
\(x\) - difference: \(3-(-9)=3 + 9=12\)
\(y\) - difference: \(10-(-4)=10 + 4=14\)
So \(d=\sqrt{12^2+14^2}=\sqrt{144 + 196}=\sqrt{340}\)
Simplify \(\sqrt{340}=\sqrt{4\times85}=2\sqrt{85}\approx 18.44\)

Answer:

The length of line \(AB\) is \(2\sqrt{85}\approx18.44\)