Question

1. find the horizontal and vertical distances from capella to ursa. show your work. include units in your answer.
2. use the distance formula, $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$, to determine how many feet of cable are needed to create the cable - car route from capella to ursa. show your work, and round your answer up to the nearest whole number. include units in your answer.

Explanation:

Step1: Identify coordinates

Capella: $(x_1,y_1)=(80,9800)$, Ursa: $(x_2,y_2)=(3900,7125)$

Step2: Calculate horizontal distance

Horizontal distance $=x_2 - x_1=3900 - 80 = 3820$ ft

Step3: Calculate vertical distance

Vertical distance $=y_1 - y_2=9800 - 7125 = 2675$ ft

Step4: Calculate cable - length using distance formula

$d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}=\sqrt{(3900 - 80)^2+(7125 - 9800)^2}=\sqrt{3820^2+(- 2675)^2}=\sqrt{14592400 + 7155625}=\sqrt{21748025}\approx4663$ ft

Answer:

Horizontal distance from Capella to Ursa: 3820 ft
Vertical distance from Capella to Ursa: 2675 ft
Length of cable needed: 4663 ft