Need help on my problem set :/

[solemnseal]

1: If x²+xy+y²=7 and x+y=2, algebraically find the value of xy

2: The area of a triangle is 5. Two if its vertices are (1,2) and (4,4). Its third vertex is on the x-axis. Explain how to find all the possible coordinates of the third vertex. What are the coordinates?

3: Segments drawn form a vertex of a rectangle to points A and B on the longer side have lengths 25 and 39 respectively. If the shorter side of the rectangle has the length 15, how long AB?

 

[pka]

1: If x²+xy+y²=7 and x+y=2, algebraically find the value of xy

You know \(\displaystyle (x+y)^2=x^2+2xy+y^2=4\).
Subtract.

 

[Deleted member 4993]

1: If x²+xy+y²=7 and x+y=2, algebraically find the value of xy

2: The area of a triangle is 5. Two if its vertices are (1,2) and (4,4). Its third vertex is on the x-axis. Explain how to find all the possible coordinates of the third vertex. What are the coordinates?

3: Segments drawn form a vertex of a rectangle to points A and B on the longer side have lengths 25 and 39 respectively. If the shorter side of the rectangle has the length 15, how long AB?

Please read the post titled "Read before Posting".

We can help - we only help after you have shown your work - or ask a specific question (not a statement like "Don't know any of these")

Please share your work with us indicating exactly where you are stuck - so that we may know where to begin to help you.

 

[solemnseal]

where i'm stuck for question 2

so for question 2, I graphed the points (1,2) and (4,4) so i could see it visually. I know that to find the area of triangle it b*h/2. So, could i use the distance between the two coordinates which is radical 13 as the base? Then to get the height, i just solved the area of a triangle formula and got 10/4=2.5. Then what i was planning on doing was making an imaginary line 2.5 units away from the line i made given the 2 coordinates. How do i show how to get the third point of the triangle to be on the x-axis? I don't think my method of solving this is right...

 

[mmm4444bot]

solved the area of a triangle formula and got 10/4=2.5

This statement is confusing. What is it exactly that you think 2.5 represents?

Instead of using incomplete English sentences to describe your steps, how about posting the work?

Did you assume that the two triangles are each right-triangles? That would be an erroneous assumption.

There are many formulas for calculating a triangle's area. You may not have been taught other formulas, yet, but you're free to research and use any method if you were not provided specific instructions on how to work the problem.

Heron's Formula is one possibility, but here's another -- derived from vector math -- that lends itself to this exercise.

Let the triangle vertices (points A, B, and C) have symbolic coordinates:

(A_x , A_y)

(B_x , B_y)

(C_x , C_y)

Here is a formula for the area of triangle ABC (note the absolute value symbols):

Area = | [1/2]*[A_x(B_y - C_y) + B_x(C_y - A_y) + C_x(A_y - B_y)] |

You have these coordinates:

A(1,2)

B(4,4)

C(X,0)

Substitute into the area formula the known values for A_x, B_x, A_y, B_y, and C_y. Use symbol X for C_x.

Solve for X.

Cheers :cool: