# An isosceles triangle has sides A, B, and C with sides B and C being equal in length. If side A goes from #(5 ,1 )# to #(3 ,2 )# and the triangle's area is #12 #, what are the possible coordinates of the triangle's third corner?

Two possibilities:

Refer to the figure below

It's known that:

It's asked

Now we could use the equations of the distance between 2 points to determine

line

Distance between a point and a line

So, making

We get two equations:

(I)

(II)

Since

line

Finding the two possible answers (by combining [2] and [4] or [3] and [4]):

(I)

#2x-6.5=-x/2+15.5 => 2.5x=22=> x=8.8#

#->y=2*8.8-6.5 => y=11.1#

#=> (8.8,11.1)# (II)

#2x-6.5=-x/2-8.5 => 2.5x=-2 => x=-0.8#

#->y=2*(-0.8)-6.5 => y=-8.1#

#=> (-0.8,-8.1)#

Checking the results:

Notice that

and

Notice also that

(testing result I)

(testing result I)

(Try result II)

As it should be: all checked

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The possible coordinates of the triangle's third corner are (7, 1) and (1, 3).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- Are these two lines parallel, perpendicular, or neither? Explain. #9x+3y=8#, #3x+9y=8#
- What is the perimeter of a triangle with corners at #(6 ,5 )#, #(9 ,2 )#, and #(3 ,8 )#?
- A triangle has corners at #(4 ,1 )#, #(2 ,3 )#, and #(5 ,8 )#. How far is the triangle's centroid from the origin?
- What is the perimeter of a triangle with corners at #(9 ,5 )#, #(6 , 2 )#, and #(5 ,7 )#?
- A triangle has corners at #(6 ,7 )#, #(2 ,6 )#, and #(5 ,2 )#. How far is the triangle's centroid from the origin?

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