I need help with analytical geometry

[Ahll22]

its going to be hard to translate since Im not from usa and im doing this from Sweden. but i will do my best

i have 3 coordinates . (0.0) (1.5) and (3.a)

(1.5) and (3.a) are both just as close to (0.0) so my goal is to know the variable A( replace A with a normal number)

Hope i made this understandable my english is not the best

A (0.0)
B(1.5)
C (3.a)

So I got mt first side ( right angled triangle)
AB by (1-0)^2 + (5-0)^2
1+25=26
and the square foot of 26 is 6
So AB=6

Im now trying to figure out the side between B and C
BC= (3-1)^2 +( a-5)^2
but Im lost and i can not solve (a-5)^2

 

[LCKurtz]

its going to be hard to translate since Im not from usa and im doing this from Sweden. but i will do my best

i have 3 coordinates . (0.0) (1.5) and (3.a)

(1.5) and (3.a) are both just as close to (0.0) so my goal is to know the variable A( replace A with a normal number)

Hope i made this understandable my english is not the best

A (0.0)
B(1.5)
C (3.a)

So I got mt first side ( right angled triangle)
AB by (1-0)^2 + (5-0)^2
1+25=26
and the square foot of 26 is 6
So AB=6

[MATH]26[/MATH] is the square of the length of AB. [MATH]\sqrt{26} \ne 6[/MATH], so you have |AB| wrong.

Im now trying to figure out the side between B and C
BC= (3-1)^2 +( a-5)^2
but Im lost and i can not solve (a-5)^2

You want to set |AB| = |AC|, not |BC|.

 

[Dr.Peterson]

Here is my understanding of the problem, to help others who may be trying to interpret it. and to give you a better idea of how you might translate it.

You are given three points, A=(0, 0), B=(1, 5), and C=(3, a), and you need to find the value of the variable a such that B and C are equidistant from A (that is, |AB| and |AC| are the same distance). Then triangle ABC will be isosceles. (At first I thought you wanted it to be a right triangle.)

You have found length |AB| as sqrt(26), using the distance formula (Pythagorean theorem); this is actually about 5.099.

Now you need to write an equation that says that |AC| = |AB|. This will be easier if instead you use |AC|² = |AB|². This way, you will not need square roots.

Let us know what you can do after making these corrections.