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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

Presented By
Sarthak Parihar

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Coordinate Geometry
Definition
Grid – A pattern of horizontal and vertical lines, usually forming squares.
Definition
Coordinate grid – a grid used to locate a point by its distances from 2 intersecting straight lines.
Definition
x axis – a horizontal number line on a coordinate grid.
Hint
x is the shortest and likes to lie down horizontally.
Definition
y axis – a vertical number line on a coordinate grid.
Hint
y is the tallest and stands upright or vertically.
Definition
Coordinates – an ordered pair of numbers that give the location of a point on a grid. (3, 4)
Hint
The first number is always the x or first letter in the alphabet. The second number is always the y the second letter in the alphabet.
How to Plot Ordered Pairs
Step 1 – Always find the x value first, moving horizontally either right (positive) or left (negative).
How to Plot Ordered Pairs
Step 2 – Starting from your new position find the y value by moving vertically either up (positive) or down (negative).
How to Find Ordered Pairs
Step 1 – Find how far over horizontally the point is by counting to the right (positive) or the left (negative).
How to Find Ordered Pairs
Step 2 – Now count how far vertically the point is by counting up (positive) or down (negative).
What is the ordered pair?
What is the ordered pair?
What is the ordered pair?
What is the ordered pair?
What is the ordered pair?
Four Quadrants of Coordinate Grid
When the number lines are extended into the negative number lines you add 3 more quadrants to the coordinate grid.
Four Quadrants of Coordinate Grid
If the x is negative you move to the left of the 0.
Four Quadrants of Coordinate Grid
If the y is negative you move down below the zero.
How to Plot in 4 Quadrants
Step 1 - Plot the x number first moving to the left when the number is negative.
How to Plot in 4 Quadrants
Step 2 - Plot the y number moving from your new position down 2 when the number is negative.
How to Plot in 4 Quadrants
When x is positive and y is negative, plot the ordered pair in this manner.
How to Plot in 4 Quadrants
When x is negative and y is positive, plot the ordered pair in this manner.