For problem #3, what is needed to prove a triangle is a right triangle?For problem # 5, what is a property of diagonals in a parallelogram?

1 Find the distance between each pair of 2 The distance between two towns P and points given below: Q is 2 km. On a coordinate system, a A(4, -3) and B(-1.5,5) town P has coordinates (x. 7) and Q has b A(1,-2, 10) and B(-4,0, 3). coordinates (3, 5). The values of the coordinates are given in kilometres. Find the value of x. 155 DIVIDING UP SPACE: COORDINATE GEOMETRY, LINES, VORONOI DIAGRAMS 3 The vertices of a sail are plotted on a pair 6 A tracking station lies at the origin of a of coordinate axes and have the following coordinate system with the x-axis due east. coordinates: A(-4,6), B(6,2) and C(-8,-4). the y-axis due north and the z-axis vertically Show that the triangular sail, AABC, is upwards. Two aircraft have coordinates shaped as a right-angled triangle. (20, 25, 11) and (26,31, 12) relative to the 4 A fountain has a circular shape. The diameter tracking station. of the circle has endpoints A(1,7) and BI-2, 1 a Find the distance between the two Find the circumference of the fountain. aircraft at this time The radar at the tracking station has a 5 Kari makes a kite in the form of a parallelo- range of 40 km. Determine whether it gram, EDGE, as shown in the diagram. It's will be able to detect both aircraft! diagonals [DF] and [EG] intersect at point H. She plots the vertices on a coordinate system with the following coordinates: D(3,6), G(1, 3). H(4.y) and E(x, 6). Find the values of x and y