Quadrilateral ABCD has the coordinates A(-3, 2), B(2, 5), and D(0, -3). If Quadrilateral ABCD is a square, what are the coordinates of vertex C ?

Answer 1

You will need to use Desmos Graphing Calculator to plot these points, A(-3, 2), B(2, 5), and D(0, -3).

The problem tells us that the quadrilateral ABCD is a square. In this case, we want to see where we can plot point C in order to create a square in the graph.

1.) Use the distance formula to find the length of AB.

d_AB = √[(x₂ - x₁)² + (y₂ - y₁)²] = √[(2 - (-3))² + (5 - 2)²] = √[(5)² + (3)²] = √(25 + 9) = √34 or 5.83

2.) Since the quadrilateral is a square, all sides are equal. We will use the result from the previous to find point C(x, y). We will use D(0, -3) and d_CD = √34 in our distance formula.

√[(x - 0)² + (y + 3)²] = √34

√[x² + (y + 3)²] = √34

x² + (y + 3)² = 34

The result shows the formula for the circle as part of the conic section. Graph the circle in Desmos. It has the center at (0, -3), which is the same as point D from the quadrilateral ABCD. The radius of the circle is √34 or about 5.83 units. We can determine the coordinates for vertex C by looking at the outline of the circle. We can tell that there is a point (5, 0) that will work in this formula.

5² + (0 + 3)² = 34 ⇒ 5² + 3² = 34 ⇒ 25 + 9 = 34 (This is correct)

Point C is at (5, 0) which is part of the quadrilateral ABCD.