SOLUTION: Graph the triangle enclosed by the Y-axis and the graphs of y - 3x = -2 and y + 3x = 2 Find the area of the triangle.

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Question 313871: Graph the triangle enclosed by the Y-axis and the graphs of y - 3x = -2 and y + 3x = 2 Find the area of the triangle.
Found 2 solutions by solver91311, Edwin McCravy:
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!




Substitute 0 for , then , hence -intercept is .

Substitute 0 for , then , hence -intercept is .



Substitute 0 for , then , hence -intercept is .

Substitute 0 for , then , hence -intercept is . Note that this is the same as the -intercept for the first equation, hence it is the point of intersection of the two lines represented by the two equations and therefore the third vertex of the triangle.

The other two vertexes are the -intercepts of the two equations. The base of the triangle is therefore that segment of the -axis between the two intercept points, while the altitude of the triangle is the segment between the origin and the point of intersection of the two lines.

You can either use the distance formula:



or simple inspection to determine that the measure of the base of the triangle is 4 and the measure of the altitude is .

Use these values in the formula for the area of a triangle:



where represents the measure of the base and represents the measure of the height or altitude.


John
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
Graph the triangle enclosed by the Y-axis and the
graphs of y - 3x = -2 and y + 3x = 2
Find the area of the triangle.

Draw the graphs of the lines:



First put them in slope intercept form:



Their y-intercepts are (0,-2) and (0,2) respectively,

So these are two of the vertices of the triangle we wish

to find the area of. 

We solve the system of equations to find the coordinates
wheteh they intersect, which be the third vertex of the
triangle we wish to find the area of.



Set the values of y equal:





Substituting in 






So the third point of the triangle is (0,)



Draw the graphs of the lines

 

So we wish to find the area of this triangle:

 

Take as a base b the line segement from (0,-2) to (0,2) which is
4 units long.  Take as an altitude h the line segment from (0,0) to
(,0) which is  units long.

Area of a triangle is  

A = bh 

A = ×(4)×()

A = ×(4)×()

A = 

Edwin
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