Coordinate Geometry

Question 1

Formula of:
1. Midpoint
2. Distance
3. Gradient
4. Equation of a line

Answer 1

1. [(x1 + x2)/2 , (y1 + y2)/2]
2. √(x2 - x1) + (y2 - y1)
3. m = (y2 - y1) / (x2 - x1)
4. y - y1 = m(x - x1)
   ◇ where (x1, y1) are coordinates

Question 2

Define
1. Parallel lines [2]
2. Perpendicular lines [2]
3. Perpendicular Bisector [3]

Answer 2

1. Lines that dont intersect & have same gradients
2. Lines that intersect at 90° & their gradients are negative reciprocals of one another
3. Same as 2 with the addition of lines intersection at midpoints

Question 3

Slope of line if:
1. m = +ve
2. m = -ve
3. m = 0
4. m = undefined

Answer 3

Looking from left to right…
1 going up (L to R)
2 going down (L to R)
3 is a horizontal line with its equation being its y coordinate
4 is a vertical line with its x coordinate being its equation

Question 4

Steps To find Perpendicular Bisector’s (PB) equation

Answer 4

1. Midpoint
2. Gradient
3. -ve reciprocate the gradient
4. y - y1 = m(x - x1)

Question 5

How to prove two lines are parallel?

How to find a coordinate if 3 points given and two lines are perpendicular?

E.g. Find k where A(2,3) B(4,7) C(k, 11) and AB & BC are perpendicular

Answer 5

m1 x m2 = -1

Ans of example: k = -4

Question 6

Collinear points [3]

Answer 6

Points that have:
Same gradients
Same y-int
Same equation

These points lie on the same line

Question 7

Where are same gradients are found [2]

Answer 7

Parallel lines & Collinear points

Question 8

How to find Con current point

Answer 8

Solving equations simultaneously.

Two or more lines intersecting at a common point are con current lines