Math pythag help pls!!!

Question

A river bank runs along the line x = 3 and a dog is tied to a post at the point D = (10, 5) . If the dog's leash is 25 units long (the same units as the coordinates), and if a fence were going to be placed at the edge of the river along x = 3 , name the two coordinates along the river where it would be safe for the fence to end so that the dog could not fall in the river even though he is tethered at D. How long would the fence be?

Answer 1

I like this problem. I am going to assume you know how to use the pythagorean theorem.

Firstly, we know both coordinates will have an x value of 3 because they are on the bank:

(3, y?) and (3, y?)

***This will be way easier to solve and understand if you draw it!

The post where the leash is attached is at x = 10 so 7 units from where the fence will be.

Draw a line and label its distance 7.

The leash is 25 units long.

Draw a hypotenuse from one end of the first line to where the river bank would be (where drawing the river bank would create a right triangle). Label its distance 25.

Draw this line again going the opposite direction but still toward where the river would be.

You can see there are two exact same right triangles formed from this with the hypotenuses being 25 and the short sides being 7.

25^2 + 7^2 = d^2 with d representing the distance along the river bank.

So, double this value (d) to get the fence distance

Now to get the y coordinates:

Just add or subtract d from the y coordinate of the post (given as 5)

The coordinates are (3, 5-d) and (3, 5+d)