16-03-2011, 04:06 PM
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Coordinate Geometry Questions
Distance Formula: d = (x2 - x1)2 + (y2 - y1)2
1. Find the distance between the points
(a) (0, 2) and (3, 6) (b) (-2, 3) and (4, -5) © (2, -5) and (-3, 7)
2. Find the exact length of the interval between points
(a) (2, 3) and (-1, 1) (b) (-1, 3) and (-7, 7)
3. Prove that the triangle with vertices (3, 4), (-2, 7) and (6, -1) is isosceles.
4. Show that the points (3, -4) and (8, 1) are equidistant from the point (7, -3).
5. Prove that the points X(2 , -3), Y(-1, 10 ) and Z(-6 , 5 ) all lie on a circle with centre at the origin.
6. If the distance between (a, -1) and (3, 4) is 5, find the value of a.
7. If the distance between (a, 3) and (4, 2) is 37 , find the values of a.
8. The points M(-1, -2), N(3, 0), P(4, 6) and Q(0, 4) form a quadrilateral. What type of quadrilateral is it?
Answers
1. (a) 5 units (b) 10 units © 13 units 2. (a) 13 (b) 213 6. a = 3 7. a = 10, -2
. 8. parallelogram
Midpoint Formula: M.P. = (x1 + x22 ,y1 + y22 )
1. Find the midpoint of
(a) (0, 2) and (4, 6) (b) (-5, 2) and (3, 0) © (3, 7) and (-3, 4)
2. Find the values of a and b if
(a) (4, 1) is the midpoint (a, b) and (-1, 5) (b) (3, b) is the midpoint of (a, 2) and (0, 0).
3. Show that line x = 3 is the perpendicular bisector of the interval between the points (-1, 2) and (7, 2).
4. The points A(-1, 2), B(1, 5), C(6, 5) and D(4, 2) form a parallelogram. Find the midpoints of the diagonals AC and BD. What property of a parallelogram does this show?
Answers
1. (a) (2, 4) (b) -1, 1) © (0, 112 ) 2. (a) a = 9, b = -3 (b) a = 6, b = 1 4. 4. (52 , 72 ) diagonals bisect each other
Gradient (slope) F0rmula: m = y2 - y1x2 - x1
1. Find the gradient of the line between
(a) (3, 2) and (1, -2) (b) (0, 2) and (3, 6) © (1, -4) and (5, 5) (d) (0, 4) and (3, -2)
2. The gradient of a line is -1 and the line passes through (4, 2) and (a, -3). Find the value of a.
3. Use the gradient formula to show that the points A(-1, 2), B(1, 5), C(6, 5) and D(4, 2) form a parallelogram.
4. A triangle has vertices A(3, 1), B(-1, -4) and C(-11, 4)
(a) Use the gradient formula to prove that the triangle is right angled.
(b) Use the distance formula to prove that the triangle is right angled.
Answers
1. (a) 2 (b) 43 © 94 (d) -2 2. a = 9
Equations of a Straight Line Formula: y – y1 = m(x – x1) or y = mx + b
1. Find the equation of a straight line
(a) with gradient 4 and y-intercept -1
(b) passing through the origin with gradient -3
© with gradient 4 and x-intercept -5
(d) passing through (2, 5) and (-1, 1)
(e) passing through (0, 1) and (-4, -2)
(f) parallel to the x-axis and passing through (2, 3)
(g) parallel to the y-axis and passing through (-1, 2)
(h) with gradient -2 and passing through the midpoint of (5, -2) and (-3, 4).
(i) passing through the midpoint of (0, 1) and (-6, 5) and the midpoint of (2, 3) and (8, -3).
Answers
1. (a) y = 4x – 1 (b) y = -3x © y = 4x + 20 (d) 4x – 3y + 7 = 0 (e) 3x – 4y + 4 = 0 (f) y = 3 (g) x = -1 (h) 2x + y – 3 = 0 (i) 3x + 8y – 15 = 0
