Draw the segment BC, calculate its length and mark where A can be.
Example Solution: x=2
Practice makes perfect
The triangle has three sides AB, BC, and CA. Let's begin by calculating the length of the side which endpoints we know, BC. We will calculate the lengths using the Distance Formula.
Let's now draw the segment BC in a diagram. We know that the third point, A(x,2), has the y-coordinate 2. In the diagram we also mark the line y=2.
Let's create a point P on the line y=2 where the distance from B to the line is the shortest.
Let's now calculate the distance from B to P. We can see that the point P has the same x-coordinate as B. Therefore the segment is vertical and we can use the Ruler Postulate to calculate its length.
Let's now calculate the distance from C to P. We notice that both points lie of the horizontal line y=4. Therefore we can calculate the distance using the Ruler Postulate and find that CP=3 units. Let's mark the distances, BC, BP, and CP, in the diagram.
If we create a triangle using the three points B, C, and P it would get the perimeter
P=BC+CP+PB=5+3+4=12 units
just like we want it to be. Let's draw this triangle and rename the point P to A.
The unknown x-coordinate for the point A is 2. Note that this is just one possible solution.
