Question

bradley lost his iphone, so he logged into the find my iphone app from his friends phone. the internal gps mapping system tracked the location of bradleys phone using the coordinate grid system. the gps system represented bradleys location at (1, 4) and said that the phone was 6 miles away at (6, k). use the distance formula below to create a radical equation to find the value of k so you can help locate bradleys phone. (round to the tenth place). $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

Explanation:

Step1: Substitute values into distance formula

Given \(d = 6\), \((x_1,y_1)=(1,4)\), \((x_2,y_2)=(6,k)\).
\(6=\sqrt{(6 - 1)^2+(k - 4)^2}\)

Step2: Simplify the equation

\(6=\sqrt{25+(k - 4)^2}\)
Square both sides: \(36=25+(k - 4)^2\)

Step3: Solve for \((k - 4)^2\)

\((k - 4)^2=36 - 25=11\)

Step4: Solve for \(k\)

\(k-4=\pm\sqrt{11}\)
\(k = 4\pm\sqrt{11}\)
\(\sqrt{11}\approx3.3\)
\(k_1=4 + 3.3=7.3\), \(k_2=4-3.3 = 0.7\)

Answer:

\(k = 0.7\) or \(k = 7.3\)