graph each set of lines to form a triangle. find the area and perimeter.

y=2, x=5 , and y=x

Answer is Area = 4.5 units Perimeter = 6 + square root of 2.

I don't know how to graph this. What does y=x mean?

draw a horizontal line at y=2

draw a vertical line at x=5
draw a sloping line from the origin, where every point y=x. For example, 5,5 is on this line, as is 3,3

Well, if you don't know how to graph y=x, don't worry, I'm here to help!

When you have the equation y=x, it means that every point on the graph will have the same x and y coordinates. In other words, the x and y values will be equal.

To graph y=x, let's start by picking some points.

If we choose x=0, then y would also be 0 because y=x. So, we have one point at (0, 0).

Similarly, if we choose x=1, y would also be 1. So, we have another point at (1, 1).

We can continue this for different values of x, and we'll see that all the points lie on a diagonal line that passes through the origin and has a slope of 1.

Now, let's look at the other lines.

The line y=2 is a horizontal line that passes through y=2 at all x values.

The line x=5 is a vertical line that passes through x=5 at all y values.

So, if we plot these lines on a graph, we'll see that they intersect at three points, forming a triangle.

To find the area and perimeter of this triangle, we can use the formula:

Area = (1/2) * base * height
Perimeter = sum of all three sides

In this case, the base and height of the triangle can be found by looking at the lengths of the sides of the triangle.

The sides of the triangle are formed by the lines y=2, x=5, and y=x.

From the graph, we can see that the base of the triangle is the side formed by the lines y=2 and y=x, and its length is 2 units.

The height of the triangle is the side formed by the lines x=5 and y=x, and its length is also 2 units.

So, the area of the triangle would be (1/2) * 2 * 2 = 2 square units.

To find the perimeter, we need to find the lengths of all three sides of the triangle.

The side formed by the lines y=2 and y=x has a length of 2 units.
The side formed by the lines y=2 and x=5 has a length of 3 units.
The side formed by the lines y=x and x=5 has a length of 3 units.

So, the perimeter of the triangle would be 2 + 3 + 3 = 8 units.

Therefore, the area of the triangle is 2 square units and the perimeter is 8 units. Or in simpler terms, the area is like the size of the triangle and the perimeter is like the distance around the triangle.

In the equation y=x, the variable "y" and "x" are equal. This means that for every value of "x", the corresponding value of "y" will be the same.

To graph this equation, you can choose some values for "x" and find the corresponding values for "y".

Let's choose some values for "x" and find the corresponding values for "y":

For x=0, y=0
For x=1, y=1
For x=2, y=2

Plot these points on a coordinate plane and connect them.

To graph the set of lines and form a triangle, we need to first understand what each equation represents.

1. y = 2: This is a horizontal line that crosses the y-axis at y = 2 and remains parallel to the x-axis.

2. x = 5: This is a vertical line that crosses the x-axis at x = 5 and remains parallel to the y-axis.

3. y = x: This is a diagonal line that passes through the origin (0,0) and has a slope of 1. It means that for every value of x, the corresponding value of y will be the same.

To graph these lines, we can plot the points where each line intersects the graph and draw lines connecting them.

1. For y = 2, we can draw a horizontal line that crosses the y-axis at y = 2.

2. For x = 5, we can draw a vertical line that crosses the x-axis at x = 5.

3. For y = x, we can plot points by substituting different values of x (e.g., x = -2, x = 0, x = 2) and finding the corresponding values of y (using y = x). Connect the plotted points to form a diagonal line passing through the origin.

Now that we have graphed the lines, we can see that they form a triangle.

To find the area of this triangle, we need to find the base and the height. The base can be found by calculating the difference between the x-coordinates of the two points where the lines intersect. In this case, the base is 5 - 0 = 5 units.

The height can be found by calculating the difference between the y-coordinate of the point where the line y = 2 intersects the y = x line. To find this point, we equate the two equations and solve for x: 2 = x. Thus, the height is 2 - 0 = 2 units.

The area of a triangle is calculated using the formula: Area = (1/2) * base * height.
Therefore, the area of this triangle is (1/2) * 5 * 2 = 5 units.

To find the perimeter, we need to measure the length of all three sides of the triangle and sum them up. From the graph, we can observe that two sides of the triangle have lengths 5 and 2 units. The third side is the diagonal line y = x, which we can calculate using the distance formula.

By applying the distance formula, the length of the diagonal side is √(5^2 + 2^2) = √29 units.

Finally, the perimeter is the sum of all three sides: 5 + 2 + √29 = 7 + √29 units.

Therefore, the answer is:
Area = 5 units
Perimeter = 7 + √29 units.