How do i check this?

Question

Take the two equations [y=2x+3]and [y=5-x]. If the intersection of the functions is one point of a triangle & the other two points are when the equations have an x-value of 5… What are the three points? What are the three distances that make the triangle? Please draw a picture to go with your problem.

Answer 1

First, lets find the x value at the intersection of the two equations.

 

2x + 3 = 5 - x

 

 

Solving this equation for x, we have

 

3x = 2

 

  x = 2/3

 

The first point of the triangle occurs at the point (2/3 ,13/3)  .  Then the other two points will meet the lines at x=5.  Therefore, you have a vertical line at x=5 intersecting the two given lines.  Consider this when drawing your graph.

 

Second point = (5, 2(5) + 3) = (5, 13)

Third point = (5, 5 - 5) = (5, 0)

 

 

Now that you have your points, use the distance formula 3 times to find the distances between the different points.

Answer 2

It's beyond my power to draw this picture, but when you find the coordinates of the three points, you can plot them and connect them to form the desired triangle.

 

First equation, when x=5, yields y = 13 so there's one point: (5,13)...call it A

Second equation yields y = 0 so a second point is(5,0)...call it B.

 

Now let's find the intersection of those two lines specified by y = ...

Let's just set those two y's equal: 2x+3 = 5-x     3x = 3     x = 1  so here's the third point: C(1,4).

 

Now you can draw the triangle and, using different pairs of coordinates, and the distance formula, you'll be able to calculate side lengths AB, AC, BC.