A quadrilateral is formed by the four lines where y=5, x=8, y=2x-5, and y=-3. Find the area of the quadrilateral
Did you actually draw the lines? The area enclosed is a trapezoid with
height = 8
top base = 3
bottom base = 7
So now you can get the area
How would you for the line?
To find the area of the quadrilateral formed by the given lines, we need to determine the vertices of the quadrilateral.
Given the four lines:
1. y = 5
2. x = 8
3. y = 2x - 5
4. y = -3
Let's analyze each line to find the points of intersection:
1. y = 5:
Since this line has a constant y-coordinate of 5, it is parallel to the x-axis. It intersects the y-axis at (0, 5).
2. x = 8:
This vertical line has a constant x-coordinate of 8. It does not intersect the y-axis but passes through all points with an x-coordinate of 8.
3. y = 2x - 5:
This line has a slope of 2 and a y-intercept of -5. To find the x-coordinate when y = 5, we can substitute y = 5 into the equation:
5 = 2x - 5
2x = 10
x = 5
So, this line intersects the x-axis at (5, 0).
4. y = -3:
This horizontal line has a constant y-coordinate of -3. It intersects the y-axis at (0, -3).
Now that we have the four points of intersection: (0, 5), (8, 0), (5, 0), and (0, -3), we can plot them on a coordinate plane to visualize the quadrilateral.
To find the area of the quadrilateral, we can divide it into two triangles and then sum the areas of both triangles.
Triangle 1: The base is the line segment from (0, -3) to (0, 5) along the y-axis. The height is the horizontal distance between the y-axis and (5, 0).
Area of triangle 1 = (base * height) / 2 = (8 - 0) * 5 / 2 = 20.
Triangle 2: The base is the line segment from (0, -3) to (8, 0) along the x-axis. The height is the vertical distance between the x-axis and (0, 5) or (0, 0).
Area of triangle 2 = (base * height) / 2 = 8 * 3 / 2 = 12.
The total area of the quadrilateral is the sum of the areas of both triangles: 20 + 12 = 32 square units.