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Magazine Problem 7
Complete an analytic proof for each theorem. The line segments that join the midpoints of the consecutive sides of a quadrilateral form a parallelogram.
Problem 22
Apply the Midpoint Formula. A circle has its center at the point \((-2,3) .\) If one endpoint of a diameter is at \((3,-5),\) find the other endpoint of the diameter.
Problem 24
Use the Distance Formula to show that the circle with center \((0,0)\) and radius length \(r\) has the equation \(x^{2}+y^{2}=r^{2}\).
Problem 27
Draw the line described. Through \((3,-2)\) and with \(m=2\)
Problem 29
Use graphing to find the point of intersection of the two lines. $$2 x+y=6 \text { and } 3 x-y=19$$
Problem 31
There are two points on the \(y\) axis that are located a distance of 6 units from the point \((3,1) .\) Determine the coordinates of each point.
Problem 39
Quadrilateral EFGH has the vertices \(E(0,0), F(a, 0)\) \(G(a+b, c),\) and \(H(2 b, 2 c) .\) Verify that \(E F G H\) is a trapezoid by showing that the slopes of two sides are equal. (GRAPH CANNOT COPY).
