A triangle that has two sides of equal length is called isosceles. Make up an example of an isosceles triangle, one of whose vertices is (3,5). If you can, find a triangle that does not have any horizontal or vertical sides.

Question

calculusxy · Answer

@agent0smith

calculusxy · Answer

I mainly need help with finding a triangle that does not have horizontal or vertical sides. What does that mean?

calculusxy · Answer

that seems logical

agent0smith · Answer

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Distance between (3, 5) and (a, 0) must equal distance between (3, 5) and (c, d) for it to be isosceles.

Pick a value of $a$, then you can work on finding $c$ and $d$ using distance formula.

You'll be able to also pick a reasonable value of $c$, once you've found the (3, 5) and (a, 0) distance.

calculusxy · Answer

Could I do something with the pythagorean theorem?

agent0smith · Answer

Pick a value of a, then find the distance between (3, 5) and (a, 0).

calculusxy · Answer

ok

calculusxy · Answer

i chose that a =1 and i had the distance of $\sqrt{29}$

agent0smith · Answer

Now pick a reasonable value of c (it must be somewhat close to x=3, within sqrt29 units, or else the triangle won't be isosceles)

Distance between (3, 5) and (c, d) will equal to sqrt 29, solve for d.

calculusxy · Answer

how did you figure out that the value of c needs to close to x = 3?

agent0smith · Answer

Draw it and find out. If you make it too far away, will it be isosceles?

calculusxy · Answer

I am confused. If x = 3, it would be right underneath the point (3,5).

calculusxy · Answer

I chose x = 5

agent0smith · Answer

You said you didn't want horizontal or vertical lines, so why would you pick x=3?

agent0smith · Answer

Distance between (3, 5) and (c, d) will equal to sqrt 29, solve for d.

calculusxy · Answer

$\sqrt{29} = \sqrt{(3-5)^2 + (5-d)^2}$

calculusxy · Answer

$$(\sqrt{29})^2 = (\sqrt{3-5)^2 + (5-d)^2})^2 $$
$29 = 4 + (5-d)^2$

calculusxy · Answer

Then I get that d = 0, 10

agent0smith · Answer

Yep.

calculusxy · Answer

But how do I know which one to choose from?

agent0smith · Answer

Well, they both work to make a triangle...but you didn't want vert/horiz lines... so you should be able to choose based on that.

calculusxy · Answer

If i have y = 0 then i don't think that it would work because it would have horizontal and vertical sides. I guess 10?

calculusxy · Answer

would that be correct @agent0smith ?

agent0smith · Answer

Sure. Draw them and it should look isosceles.

calculusxy · Answer

Thank you! Can you help me with another question please?

calculusxy · Answer

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