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Question 1014326: The three lines y=x-1, y=4-2x, y=-x-5 intersect to form a triangle. Determine the coordinates of the vertices of the triangle.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! you need to solve 3 sets of 2 equations that need to be solved simultaneously.
this will get you the 3 intersection points.
first set is y = x-1 and y = 4-2x
second set is y = x-1 and y = -x-5
third set is y = 4-2x and y = -x-5
first set:
start with y = x-1 and y = 4-2x
since both x-1 and 4-2x are equal to y, you can set them equal to each other and solve for x.
start with x-1 = 4-2x
add 2x to both sides of the euation and add 1 to both sides of the equation to get 2x + x = 4 + 1
combine like terms to get 3x = 5
divide both sides of the equation by 3 to get x = 5/3 = 1 and 2/3 = 1.666...
when x = 5/3, y = x-1 gets you y = 5/3 - 1 which gets you y = 2/3.
you have x = 1.67 and y = .67.
your intersection point is (1.67,.67) rounded to 2 decimal places.
second set:
start with y = x-1 and y = -x-5
since both x-1 and -x-5 are equal to y, you can set them equal to each other to get x-1 = -x-5
add x to both sides of the equation and add 1 to both sides of the equation to get x + x = -5 + 1
combine like terms to get 2x = -4
divide both sides by 2 to get x = -2
when x = -2, y = x-1 gets you y = -2-1 which gets you y = -3
you have x = -2 and y = -3.
your intersection point is (-2,-3)
third set:
start with y = 4-2x and y = -x-5.
since both 4-2x and -x-5 are equal to 6, you can set them equal to each other to get 4-2x = -x-5.
add x to both sides of the equation and subtract 4 from both sides of the equation to get -2x + x = -5 - 4.
combine like terms to get -x = -9
multiply both sides of the equation by -1 to get x = 9
when x = 9, y = 4-2x gets you y = 4-18 which gets you y = -14.
you hve x = 9 and y = -14.
your intersection point is (9,-14)
you have 3 intersection points which form your triangle.
on the graph, the intersection points are the coordinate points.
they are:
(1.67,.67)
(-2,-3)
(9,-14)
i graphed the three equations and marked the intersection points.
they agree.
on the graph 1.67 is shown as 1.667.
that's the same x-coordinate with different rounding applied.
here's the graph.
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