Starter Find the midpoints of the line segments

Starter Find the midpoints of the line segments joining (6, -2) and (1, 2) midpoint = (3½, 0) (3, -2) and (1, -6) midpoint = (2, -4)

Prove that the points A(-1, -2), B(1, 1), C(8, -1) and D(6, -4) are the vertices of a parallelogram. (HINT: find the lengths of all four sides and the diagonals) AB = 3. 6 units BC = 7. 3 units DC = 3. 6 units AD = 7. 3 units AC = 9. 1 units BD = 7. 1 units Length of AB = length of CD and length of BC = length of AD. The lengths of the diagonals are different, so therefore the shape is a parallelogram

Note 3: Gradient (slope) • measures the steepness of a line • is defined as • is positive if the line leans to the right • is negative if the line leans to the left • is zero if the line is horizontal • is not defined if the line is vertical RISE RUN

Examples: 4 cm 2 cm Leans left, so m is negative! 8 8 3 2 5 km 3 km

C y 2 Let A (x 1 , y 1 ) and B (x 2 , y 2 ) be any two points (y 2 y 1 (x 2 – x 1) B (x 2 , y 2 ) - y 1) A (x 1 , y 1 ) The GRADIENT of AB is given by m= x 2 x 1 rise is y 2 – y 1 run is x 2 – x 1

Example: (x 1, y 1) Find the gradient of the line joining points A(4, 3) and B(1, – 3) A(4, 3) • M= • B(1, – 3) (x 2, y 2) C

Parallel lines have the same gradient Perpendicular lines gradients are the negative reciprocals of each other m 1 x m 2 = -1 Example: If line AB has a gradient of 2/3, and line CD is perpendicular to line AB, what is the gradient of CD? Gradient of CD = -3/2 Points are collinear if they lie on the same line – their gradients are equal

Page 262 Exercise 8 C