SOLUTION: The equations y = 2x - 1 and y = -1/2x + 4 intersect in Quadrant I. Find the area of the triangle formed with this point of intersection and the two y-intercepts of the lines.

Algebra ->  Surface-area -> SOLUTION: The equations y = 2x - 1 and y = -1/2x + 4 intersect in Quadrant I. Find the area of the triangle formed with this point of intersection and the two y-intercepts of the lines.      Log On


   

Question 1050683: The equations y = 2x - 1 and y = -1/2x + 4 intersect in Quadrant I. Find the area of the triangle formed with this point of intersection and the two y-intercepts of the lines.
Found 3 solutions by ewatrrr, Fombitz, josmiceli:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!

A = (1/2)bh
A = (1/2)5*2 = 5 units^2

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Graphically,
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The y intercepts are -1 and 4 respectively so the base of the triangle is B=4%28-1%29=5
The height of the triangle is 2.
You can also find this using the intersection point of the two lines by setting them equal to each other,
2x-1=-%28x%2F2%29%2B4
4x-2=-x%2B8
5x=10
x=2
So,
A=%281%2F2%29BH=%281%2F2%29%285%29%282%29=5

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Find the point of intersection
+y+=+2x+-+1+
+y+=+-%281%2F2%29%2Ax+%2B+4+
---------------------
By substitution:
+2x+-+1+=+-%281%2F2%29%2Ax+%2B+4+
Multiply both sides by +2+
+4x+-+2+=+-x+%2B+8+
+5x+=+10+
+x+=+2+
and
+y+=+2x+-+1+
+y+=+2%2A2+-+1+
+y+=+3+
----------------------------
The intersection is at ( 2,3 )
----------------------------
Now find the y-intercepts
by setting +x+=+0+
-----------------------------
+y+=+2x+-+1+
+y+=+2%2A0+-+1+
+y+=+-1+
( 0, -1 )
----------------
+y+=+-%281%2F2%29%2Ax+%2B+4+
+y+=+-%281%2F2%29%2A0+%2B+4+
+y+=+4+
( 0, 4 }
--------------------
The distance between the 2 y-intercepts is:
+abs%28+4+-%28-1%29+%29+
+abs%28+5+%29+=+5+
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The height of the triangle formed is
the x-value of the intersection ( 2,3 )
which is +2+
---------------------
+A+=+%281%2F2%29%2A5%2A2+
+A+=+5+
The area is 5 square units
------------------------
Here's the plot of the lines:
+graph%28+400%2C+400%2C+-10%2C+10%2C+-10%2C+10%2C+2x+-+1%2C+-%281%2F2%29%2Ax+%2B+4+%29+