Show that the following points are the vertices of a rectangle :
(i) `A(4, 2), B(0, -4), C(-3, -2), D(1, 4)`
(ii) `A(1,-1), B(-2, 2), C(4, 8), D(7, 5)`

Show that the following points are the vertices of a rectangle. (i) A(-4, -1), B(-2, -4), C(4, 0) and D(2, 3) (ii) A(2, -2), B(14, 10), C(11, 13) and D(-1, 1) (iii) A(0, -4), B(6, 2), C(3, 5) and D(-3, -1)

Name the quadrilateral formed, if any, by the following points, and give reasons for your answers: A(-1,\ -2),\ \ B(1,\ 0),\ \ C(-1,\ 2),\ \ D(-3,\ 0) (ii) A(-3,\ 5),\ \ B(3,\ 1),\ \ C(0,\ 3),\ \ D(-1,\ -4) (iii) A(4,\ 5),\ \ B(7,\ 6),\ \ C(4,\ 3),\ \ D(1,\ 2)

Match the following and choose the correct combination from the options given : (a) {:(A, B, C, D),(3 , 1, 5, 4):} (b) {:(A, B, C, D),(1, 2, 3, 4):} (c) {:(A, B, C, D),(2, 1, 3, 4):} (d) {:(A, B, C, D),(3, 1, 5, 2):}

Show that the points A(2,3,5),B(-4,7,-7),C(-2,1,-10) and D(4,-3,2) are the vertices of a rectangle.

Show that the point (1,2,3) is common to the lines which join A(4,8,12) to B(2,4,6) and C(3,5,4) to D(5,8,5)

Show that the points A(3,5),B(6,0), C(1,-3) and D(-2,2) are the vertices of a square ABCD.

Which types of the following functions are ? (i) {(a,1),(b,1),(c,1),(d,1),(e,1)} (ii) {(3,2),(6,4)(9,2),(12,4)} (iii) {(a,1),(b,2),(c,3),(d,4)}.

Show that the points (4,7,8),(2,3,4),(-1,-2,1) ,(1,2,5) are the vertices of a paralelogram.

Show that the DeltaABC with vertices A ( 0,4, 1) , B ( 2, 3, -1) and C ( 4,5,0) is right angled.

Find the angles of a triangle whose vertices are A(0,\ -1,\ -2),\ B(3,\ 1,\ 4)a n d\ C(5,\ 7,\ 1)dot