Coordinate Geometry

Question 1

Distance between two points

Answer 1

d = root[ (x2 - X1)^2 + (y2-y1)^2]

Question 2

Midpoint

Answer 2

M = (X1 + x2 , y1 + y2)
——- ——-
2 2

Question 3

Gradient

Answer 3

Run

X2 - X1

Question 4

Angle of inclination

Answer 4

M = tan theta

Eg gradient is 2

            M= tan theta
            2 = tan theta Tan ^-1 x 2 = theta
     Theta = 63.43°

Question 5

Parallel lines

Answer 5

Same gradients

M1 = m2

Question 6

Perpendicular lines

Answer 6

The gradients are negative reciprocals of each other (flip the fraction and change the sign)

M1 x m2 = -1

Question 7

Horizontal and vertical lines

Answer 7

Horizontal- y=c

Vertical- x=c

Where c is a constant number

Question 8

Gradient intercept form

Answer 8

Y= mx + b

Question 9

General form

MUST ALWAYS HAVE POSITIVE X AND NO FRACTIONS

Answer 9

0 = x + y + constant

Eg 0= 3x - 2y + 12

Question 10

Point gradient form

Answer 10

Y - y1 = m(x - X1)

Or two point gradient form (m is replaced with gradient formula)