Answer:
400 units^2
Step-by-step explanation:
Its a bit much but.....
You have 3 lines that must intersect somewhere on those lines to form a triangle.
You know from the lines y = 23 and x = -6, that those two lines will intersect at point (-6, 23) and also form the opposite and adjacent legs of a right triangle.
The line y = 2x - 5 has a slope of 2 and a y-intercept of 5.
To find intersecting points, set two equations equal to each other (rearrange first) and solve for the unknown value:
y - 2x + 5 + 23 = y
-2x = -28
x = 14
So, the line y = 2x - 5 will intersect the line y = 23 at the point (14, 23)
Now to find where the line will intersect x = -6:
y = 2x - 5
0y = -2x - 12
y = -17
So, the line y = 2x + 5 will intersect the line x = -6 at point (-6, -17)
We know that the distance of a line is defined as x2 - x1 for horizontal lines.
We know that the distance of a line is defined as y2 - y1 for vertical lines.
So the distance of the x = -6 line is the y-values for the points were the line y = 2x + 5 intersects and where the line y = 23 intersects.
23 - (-17) = 23 + 17 = 40
The distance of the line x = -6 is 40 units.
14 - (-6) = 14 + 6 = 20
The distance of the line y = 23 is 20 units.
We know the area for a right triangle formula is A = ab/2:
A = 20(40)/2
A = 800/2
A = 400 units2
The area of the triangle formed by the the three lines is 400 units2
