1Use Pythagoras' theorem to check whether these triangles are right angled: (a) \( \sqrt{7} \), 4, \( \sqrt{10} \) (b) \( \sqrt{10} \), 3, \( \sqrt{19} \) (c) 4, 11, 12 (d) 5, 5, \( \sqrt{34} \) (e) 9, 12, 15 (f) 5, 6, 7
2Find x in these right angled triangles: (a) sides x and 12 cm, hypotenuse 13 cm (b) sides 48 cm and 14 cm, hypotenuse x (c) sides 21 cm and 72 cm, hypotenuse x (d) sides 6 in and 8 in, hypotenuse x (e) sides x and 15 ft, hypotenuse 25 ft (f) sides x and \( \sqrt{5} \) cm, hypotenuse \( \sqrt{8} \) cm (g) sides 15 cm and 8 cm, hypotenuse x (h) sides 11 m and x, hypotenuse 16 m (i) sides 7 cm and 24 cm, hypotenuse x
3Find the distance between each of these pairs drawn on the graph: (a) (-6, 3) and (-2, 3) (b) (4, 5) and (4, 1) (c) (2, 2) and (7, 2) (d) (10, 5) and (10, 1) (e) (2, -2) and (7, -2)
4Find the distance between the given points: (a) (4, -7) and (-1, 5) (b) (-3, 4) and (4, 3) (c) (1, -2) and (5, -6) (d) (1, 7) and (1, 1) (e) (2, 7) and (4, 9) (f) (-8, 7) and (-3, 4)
5Point A cuts the X-axis at -8 and point B cuts the Y-axis at 6. Find the distance AB.
6On graph paper a cat is at the point (-4, 1) and a mouse is at the point (3, 3). Find the distance between them.
7Prove that the points A(-4, 0), B(-4, -4), C(2, -4) and D(2, 0) are the vertices of a rectangle.
8On a map, Waling and Kathmandu are at (4, 7) and (7, 3). What is the distance between those points on the map? If 1 unit stands for 55 km, find the real distance between Waling and Kathmandu.
9Find the lengths of all three sides of the triangle with vertices P(1, 6), Q(4, 1) and R(-4, 3), and say what kind of triangle it is.
10If A(2, -1), B(3, 4), C(-2, 3) and D(-3, -2) are the vertices of the rhombus ABCD, find the lengths of its diagonals AC and BD.
11If P(9, 12) lies on the circumference of a circle whose centre is Q(1, 6), what is the radius of the circle? Does the point (-7, 0) lie on that circumference?
12Find the distance of point A and point B from the origin O, where A = (-7, 7) and B = (7, -7).
13If the distance between P(0, 6) and Q(a, 0) is 6 units, what is the value of a?
14To reach point B from the origin you go 4 units right and 3 units up. What are the coordinates of B, and how long is OB?
15A student wrote \( \sqrt{(7 - 3) + (2 - 5)} \) while finding the distance between (3, 5) and (7, 2). What went wrong, and what is the right answer?
16Check whether the triangle with vertices A(0, 0), B(6, 0) and C(6, 8) is right angled by finding its side lengths.