Recall that an isosceles trapezoid is a trapezoid that has congruent non-parallel sides.
Three possibilities:
D(7,1)
D(-2,-2)
D(-0.2,3.4)
Practice makes perfect
Let's start by plotting the three points in a coordinate plane. To make it easier to talk about the segments, we will label the points A, B, and C.
Notice that a trapezoid is a quadrilateral with one pair of parallel sides. Depending on how we connect the points and which segments make up the pair of parallel sides, we get three different answers. Let's start by connecting A and B as well as B and C.
Answer #1
If the pair of parallel sides includes BC, its opposite side must be a horizontal segment along y=1. Let's add that to the diagram.
To determine where we should place D along the ray we just drew, we notice that the exercise tells us that this is an isosceles trapezoid. This means the trapezoid's nonparallel sides are congruent. To determine how to draw the second leg, we will add some additional information to the diagram.
To create the isosceles trapezoid, we have to draw the final side so that we get a triangle that is congruent to the purple triangle. Since we know the legs of the purple triangle, we can do that.
Answer #2
If the pair of parallel sides includes AB, its opposite side must have the same slope as AB. Therefore, we will start by calculating the slope of AB.
We are looking for the point D(x,y) on the line that has a distance of 3 units from ( -2, 1).
3=sqrt((x-( -2))^2+(y- 1)^2)
⇕
3=sqrt((x+2)^2+(y-1)^2)
Notice that the parallel side to AB has an equation of y=x. To solve this equation, we will use the fact that y=x.
When x=-2 or x=1, the distance is 3 units. However, x=1 would make the quadrilateral a rhombus. Therefore, D should be placed on the ray where x=-2. This makes it a trapezoid.
Answer #3
We can also draw the first two sides by drawing AC and BC.
In this case, the pair of parallel sides can only include AC. Therefore, we will start by calculating the slope of AC.
The ray's equation is y=0.5x+3.5. Now we can draw the parallel side to AC as a ray.
Again, the distance from B to C is 3 so we will set up an equation using the Distance Formula.
3=sqrt((x-( -2))^2+(y- 1)^2)
⇕
3=sqrt((x+2)^2+(y-1)^2)
To solve this equation, we will use the fact that y=0.5x+3.5.
From the graph, we can see that x=-5 is too far to the left to be the solution we need. Let's substitute x=0.2 into our equation for the line to find the corresponding y-value.
