Help with various difficult line problems

[CraftyCat3]

Hello I'm new to this site and I was just looking for help on some advanced line problems my teacher assigned us.

1.If a, b > 0 and the triangle in the first quadrant bounded by the Cartesian coordinate system and the graph of ax+ by = 10 has an area of 5 find ab.

This jpg shows my work in order to reach the answer the ab which is ab=10.
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I apologize for failing to read and follow the forum rules. I will make sure I do next time. I finished all of the problems but i just uploaded my work for the first one. Thank-you for the help.

 

[Deleted member 4993]

Hello I'm new to this site and I was just looking for help on some advanced line problems my teacher assigned us. I was able to do most of them but there are seven which I am completely lost on. I would really appreciate any help.

1.If a, b > 0 and the triangle in the first quadrant bounded by the Cartesian coordinate system and the graph of ax+ by = 10 has an area of 5 find ab.

2. Lines with slopes -1 and -2 are drawn through the first quadrant point (a,b) forming one triangle with a side on
the x-axis and one triangle with a side on the y-axis. What is the total area of the two triangles (write your
answer explicitly in terms of a and b)?

3.If a line intersects the x-axis at 'r' and the y-axis at '1/r',at what point (x,y) does it intersect the line y=x.

4.Determine all values of 'c' s.t. the lines x - y : 2 and cx + y : 3 intersect in Ql (note x-y axes are not considered Ql.)

5.The lines L and K are symmetric to each other with respectto the line y = x. If the equation of line L is y = ax
+ b with 'a' and 'b' not equal to 0, then the equation of K is?

6.A triangle whose area is 4 is bounded by the two coordinate axes and also by the line whose slope is 4 and
whose y-intercept is b. lf b > 0, what is the value of b?

7.In the xy-plane, consider the L-shaped region bounded by horizontal and vertical segments with vertices at
(0,0), (0,3), (3,3), (3,1), (5,1), and (5,0). Find the slope of the line through the origin that divides the area of this
region exactly in half?
-I can draw this shape but I have no idea how to make a line that cuts it in half

8. Let S be the set of points (a,b) in the coordinate plane, where each of a and b may be -1, 0, or 1. How many
distinct lines pass through at least two members of S?

Hint for #3
3.If a line intersects the x-axis at 'r' and the y-axis at '1/r',at what point (x,y) does it intersect the line y=x.

Equation of the line:

\(\displaystyle \dfrac{x}{r} + \dfrac{y}{\frac{1}{r}} = 1\)

Now continue......

Please share your work with us .

If you are stuck at the beginning tell us and we'll start with the definitions such as "what is commisson"?"

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/th...217#post322217http://www.freemathhelp.com/forum/th...217#post322217

 

[JeffM]

Hello I'm new to this site and I was just looking for help on some advanced line problems my teacher assigned us. I was able to do most of them but there are seven which I am completely lost on. I would really appreciate any help.

1.If a, b > 0 and the triangle in the first quadrant bounded by the Cartesian coordinate system and the graph of ax+ by = 10 has an area of 5 find ab.

2. Lines with slopes -1 and -2 are drawn through the first quadrant point (a,b) forming one triangle with a side on
the x-axis and one triangle with a side on the y-axis. What is the total area of the two triangles (write your
answer explicitly in terms of a and b)?

3.If a line intersects the x-axis at 'r' and the y-axis at '1/r',at what point (x,y) does it intersect the line y=x.

4.Determine all values of 'c' s.t. the lines x - y : 2 and cx + y : 3 intersect in Ql (note x-y axes are not considered Ql.)

5.The lines L and K are symmetric to each other with respectto the line y = x. If the equation of line L is y = ax
+ b with 'a' and 'b' not equal to 0, then the equation of K is?

6.A triangle whose area is 4 is bounded by the two coordinate axes and also by the line whose slope is 4 and
whose y-intercept is b. lf b > 0, what is the value of b?

7.In the xy-plane, consider the L-shaped region bounded by horizontal and vertical segments with vertices at
(0,0), (0,3), (3,3), (3,1), (5,1), and (5,0). Find the slope of the line through the origin that divides the area of this
region exactly in half?
-I can draw this shape but I have no idea how to make a line that cuts it in half

8. Let S be the set of points (a,b) in the coordinate plane, where each of a and b may be -1, 0, or 1. How many
distinct lines pass through at least two members of S?

You clearly did NOT read Read Before Posting. I suggest you do so.

OK Now that you have read that you understand that your post has violated the rules of this site in numerous ways. Most important procedurally is the rule against more than one problem per thread. I am going to treat this as a post about problem 1. Most important substantively is the rule that this site gives help, not answers. We help you figure out the answer; we are not going to be there to give you answers on your tests.

A lot of math involves figuring out what you already know that is relevant to what you want to find out. So let's figure out what you know that may be relevant. This largely a process of thinking systematically; there is no magic recipe, just organizing your thoughts.

Problem: If a, b > 0 and the triangle in the first quadrant bounded by the Cartesian coordinate system and the graph of ax+ by = 10 has an area of 5 find ab.

The first thing I see is that for you to find ab, you may have to find a and b separately because neither equals zero. Do you follow that?

What clues do you have about a and b? Well you have a triangle and its area. Let's consider the triangle first. What do you know about triangles? They have three sides. Unfortunately, this triangle is described in a rather stupid way. What is meant is that one side of the triangle is the x axis, one side is the y axis, and one side is the line graphing the equation ax + by = 10. Do you agree?

It would help to have a sketch of the triangle so you can SEE what you are doing.

Where does the graph of ax + by = 10 intersect the x axis?

Where does the graph of ax + by = 10 intersect the y axis?

Now you can sketch the triangle. Can you solve the rest of the problem on your own?

If you can, tell us the answer you get and HOW you got it so we can tell you if you are correct.

If you can't, show us what you tried.