Page 5 - Senior Math

Find the distance between the following pairs of points.
1) (3,5) and (6,4) 2) (−4,2) and (4,17)
3) (9,2) and (3,−6) 4) (4,2) and (6, −23)
5) Do the coordinates 𝐿(7, −4), 𝑀(−1, 2), and 𝑁(5, −6) form an isosceles triangle?
6) Find the perimeter of square QRST if two of the vertices are 𝑄(6, 7) and 𝑅(−3, 4).
7) If the diagonals of a trapezoid have the same length, then the trapezoid is isosceles. Find the lengths of the diagonals of the trapezoid with vertices 𝐴(−2, 2), 𝐵(10, 6), 𝐶(9, 8), and 𝐷(0, 5) and determine if it is isosceles.
8) Use vertices 𝐴(1, 7), 𝐵(3, 5), 𝐶(4, −1), and 𝐷(2, 1) to determine that the opposite sides of quadrilateral ABCD are equal in length. What kind of quadrilateral is ABCD?
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9) Given 𝐴(−3, 3), 𝐵(1, 11), and 𝐶(3, 15), show B is on 𝐴𝐶 by showing that 𝐴𝐵 + 𝐵𝐶 = 𝐴𝐶.
10) Show that 𝑃(4, 2) is equidistant from 𝐴(9, 2) and 𝐵(1, 6). 4