Coordinate Geometry.

Pawan Ramnani wrote:What is the area inscribed by the lines y =1, x = 1, y = 6-x on an xy-coordinate plane?

a) 8
b) 10
c) 12
d) 14
e) 18

When posting questions, please use the spoiler function to hide the correct answer. This will allow others to attempt the question without seeing the final answer.

First, let's graph the lines y = 1 and x = 1


At this point, we need to find the points where the line y = 6-x INTERSECTS the other two lines.

For the vertical line, we know that x = 1, so we'll PLUG x = 1 into the equation y = 6-x to get y = 6-1 = 5
Perfect, when x = 1, y = 5, so one point of intersection is (1,5)

For the horizontal line, we know that y = 1, so we'll PLUG y = 1 into the equation y = 6-x to get 1 = 6-x. Solve to get: x = 5
So, when y = 1, x = 5, so one point of intersection is (5,1)

Now add these points to our graph and sketch the line y = 5-x


At this point, we can see that we have the following triangle.

The base has length 4 and the height is 4
Area = (1/2)(base)(height)
= (1/2)(4)(4)
= 8

Answer: A