Find the shortest distance passing through P(3, 5), whose ends are touching the x and y axes.

Question

Find the shortest distance passing through P(3, 5), whose ends are touching the x and y axes.

I can't post the image but its right triangular whose midpoint is (3,5). I tried my best to copy the image by text, don't mind the dots 😅

| \

|....\

|......\ • P (3,5)

|........\

|...........\

____________

0|

a. 13.5 units

b. 12.4 units

c. 11.2 units

d. 10.6 units

e. None of the above.

My answer is 5.83 units and I'm not very of it, pls provide a step by step explanation so I could follow. Thank you ❤️

Answer 1

none of the above

c is closest though

solution is square root of ( (2x5)^2 + (2x3)^2) = sqr136= about 11.66 = about 11.7

(3,5) is the middle of the shortest length

shortest length = hypotenuse of right triangle with legs = 10 and 6

if someone misread or miscopied the 7 as a 2, then they'd make 11.2 into the correct answer, so an answer key or instructor just might make c as the correct answer

2x5.83= 11.66 = the hypotenuse. you're on the right track

5.83 is half the shortest distance= the distance from the point to the x axis and from the point to the y axis along the hypotenuse

5.83 is also the distance from the point (3,5) to the origin (0,0) = sqr(3^2 + 5^2) = sqr34 = about 5.83

that is the shortest distance from the point to both the x and y axes, simultaneously.

it depends on how you word the question, what distance you're looking for