Question

question 2 of 5 mike rides his bike to work every day. his house is located on the cartesian plane at the point h (6, 19). his work is located at the point w (1, -10), where all measurements are in kilometres. calculate the number of kilometres mike travels on his bike to work and back again. give your answer correct to 2 decimal places.

Explanation:

Step1: Recall distance formula

The distance $d$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, $(x_1,y_1)=(6,19)$ and $(x_2,y_2)=(1,- 10)$.

Step2: Calculate differences

$x_2 - x_1=1 - 6=-5$ and $y_2 - y_1=-10 - 19=-29$.

Step3: Square the differences

$(x_2 - x_1)^2=(-5)^2 = 25$ and $(y_2 - y_1)^2=(-29)^2=841$.

Step4: Sum the squared differences

$(x_2 - x_1)^2+(y_2 - y_1)^2=25 + 841=866$.

Step5: Calculate one - way distance

$d=\sqrt{866}\approx29.43$.

Step6: Calculate round - trip distance

The round - trip distance is $2d$. So, $2\times29.43 = 58.86$.

Answer:

$58.86$