Unit 3: Coordinate Geometry - Grade 9

Question 1

Gradient

Answer 1

“Steepness”; “direction”; rate of change of y with respect to x
change in y over change in x

Question 2

Rises from left to right

Answer 2

gradient is positive

Question 3

Fall from left to right

Answer 3

gradient is negative

Question 4

Horizontal

Answer 4

gradient = 0

Question 5

Vertical

Answer 5

gradient: “infinite”, “undefined” or “no gradient”

Question 6

Slope intercept form

Answer 6

y = mx + b
m: slope/gradient
b: y-intercept

Question 7

Point slope form

Answer 7

y - y^1 = m(x - x^1)
m: slope
(x^1, y^1) is a point on the line

Question 8

Standard general form

Answer 8

Ax + By = C

Question 9

Parallel line (||)

Answer 9

If two lines are parallel then the gradients are the same

Question 10

Perpendicular line

Answer 10

If two lines are perpendicular then the gradient is the negative reciprocal of the other gradient

Question 11

Simultaneous equations (by substitution)

Answer 11

to find point of intersection of two lines
- solve for x and the solve for y

Question 12

Perpendicular bisector of a point

Answer 12

1) coordinates of midpoint
2) find the gradient
- negative reciprocal
3) put into y = mx + b
4) substitute the coordinates of midpoint for x and y
5) solve for b (y-intercept)
6) insert y-intercept into y = mx + b