91Ó°ÊÓ

Use coordinate geometry to prove each statement. First draw a figure and choose convenient axes and coordinates. The diagonals of a parallelogram bisect each other.

What can you say about the slope of (a) the \(x\) -axis? and (b) the \(y\) -axis?

Use coordinate geometry to prove each statement. First draw a figure and choose convenient axes and coordinates. The diagonals of a rhombus are perpendicular. (Hint: Let the vertices be \((0,0),(a, 0),(a+b, c),\) and \((b, c) .\) Show that \(c^{2}=a^{2}-b^{2}\)

Find the slope of each side and each altitude of \(\triangle A B C\). \(A(1,4) \quad B(-1,-3) \quad C(4,-5)\)

Use slopes to show that \(\triangle R S T\) is a right triangle. \(R(-3,-4) \quad S(2,2) \quad T(14,-8)\)

Given the points \(A(-6,-4), B(4,2), C(6,8),\) and \(D(-4,2)\) show that \(A B C D\) is a parallelogram using two different methods. a. Show that opposite sides are parallel. b. Show that opposite sides are congruent.

Given: Points \(R(-4,5), S(-1,9), T(7,3)\) and \(U(4,-1)\) a. Show that \(R S T U\) is a rectangle. b. Use the distance formula to verify that the diagonals are congruent.

Given: Points \(N(-1,-5), O(0,0), P(3,2),\) and \(Q(8,1)\) a. Show that \(N O P Q\) is an isosceles trapezoid. b. Show that the diagonals are congruent.

Find the slope and \(y\) -intercept of each line. Plot the \(y\) -intercept. Then, using the slope, plot one more point. Finally, graph the line. $$y=2 x+3$$

Find the length of the longest median of the triangle with vertices \(X(-2,3), Y(6,-3),\) and \(Z(4,7)\).