S56 (5.1) Straight Line.notebook November 23, 2016missdeely.weebly.com/uploads/2/1/3/0/21307444/higher_straight_lin… · Q1. State the gradient of the line 2x + 5y = 3 Q2. State

S56 (5.1) Straight Line.notebook November 23, 2016

Daily Practice 25.10.2016

Q1. Simplify

Q2. Stat ethe limit of the recurrence relation un+1 = 0.8un + 5

Q3. Write in completed square form 3x2 + 12x + 7

Q4. State the equation of the line parallel to 3x - y = 1 and passes through

(4, -6)

L.I: Today we will be learning how to calculate the gradient of a line using tan.

Gradient Given a right - angled triangle on a coordinate grid

θ

opphyp

adjθ

The gradient is the tan of the angle that the line makes with the positive direction of the x - axis.

m = tan θ

Examples:

1. Find the angle that the line shown makes with the

positive direction of the x - axis

Gradient using Tan

(2, 5)

(-4, -2)

Examples:

2. A line makes an angle of 1350 with the positive direction of the x - axis, state the gradient of this line

Gradient


Perpendicular Gradient

a

b900

a

b

a

b

To find the gradient of the line perpendicular to m1 just turn the gradient upside down and change the sign.

If two lines are perpendicular, then the product of their gradients is -1.

m1 x m2 = -1


Examples:

1. Calculate the gradient of the line perpendicular to the line joining A(-1, 4) and B(5, -3)


Examples:


2. State the equation of the line perpendicular to 7x + y + 3 = 0 that passes through (0, 5)

Examples:


3. Given the points B(5, 3), D(3, 7) & C(-1, 5), that the line BD is perpendicular to the line CD.

Homework Online due 16.6.2015 (Gradient)



Q1. Find the equation of the line perpendicular to y = -3x + 2 that passes

through the point (4, 5)

Q2. State the gradient of the line 3y + 5x - 4 = 0

Q3. State the angle that the line y = 1.5x + 2 makes with the positive direction

of the x - axis

Q4. If f(x) = 3x - 2 and g(x) = x2 - 1, find the value of g(f(x))

L.I: Today we will be learning about Collinearity

and Distance Between Two Points.

Collinearity

Points are said to be collinear if they lie on the same straight line.

A

B

C

To prove that points are collinear, show that they have the same gradient & share a common point.

Collinearity

Examples:

1. A(-2, -5) B(2, -1) and C(8, 5). State whether these points are collinear

2.(i) Calculate the gradient of P(-5, 1) and Q(3, 7)

(ii) Which point Z(-2, 5) or S(-1, 4) lies on the line PQ?Ex. 1B Q1-3

Ex. 1B Q2.

Which sets of the following points are collinear?

(a) A(-5, -3), B(-1, 0) and C(7, 6)

(b) P(2, -6), Q(-1, 3) and R(-3, 8)

(c) S(-5, -6), T(2, -2) and U(10, 2)

(d) E(6, -4), O(0, 0) and F(-9, 6)

Distance between two points

To find the distance between two

points (length of AB).

A (x1, y1)

B(x2, y2)

Example:

Calculate the distance between A(-2, 3) and B(2, 1)


Distance between two points

To find the distance between two points.

A

B

Distance between two pointsQuestions: Find the distance between the following

i) (-5, -4) and (2, 1)

ii) (0, -3) and (1, 4)

iii) (0, -2) and (5, 0)

iv) (-7, 8) and (2, -6)

Find the equation of the following lines:

1) Parallel to the x-axis and passing through the point (3, -2)

2) Perpendicular to the x-axis and passing through the point

3) Passing through the points (-3, 8) and (-3, -5)

4) Passing through the points (-7, -2) and (4, -2)

5) Passing through (3, -4) and perpendicular to the line

passing through the points (1, 3) and (-6, 3).

The equation of horizontal and vertical lines Daily Practice 27.10.2016

Q1. State the gradient of the line 2x + 5y = 3

Q2. State the equation of the line that passes through (0, 8) and is perpendicular to the line y = -x + 2

Q3. Given that the function f(x) = 2x + 3 passes through the point (1, b). State the value of b

Q4. State the equation of the line passing through the points (-3, 8) and (-3, -5)

L.I: Today we will be learning about midpoint and perpendicular bisectors.

The mid - point is half-way point between two points on a line.

P (-2, 1)

Q (2, 5)

Find the mid-point between each pair of points:

1) A(2, 3) & B(8, 11)

2) C(1, -8) & D(-9, -12)

3) E(-3, 12) & F(5, - 2)


The Mid-point

The midpoint of the points (x1 , y1) and (x2 , y2) is Examples:

Find the mid-point between the following pairs of coordinates

a) A(1, 3) & B(7, 15)

b) C(-4, 9) & D(6, -13)

The Mid-point

Perpendicular Bisectors

A perpendicular bisector is a line that bisects another line at right angles.

CD is the perpendicular bisector

of the line AB

C

DA

B

Example:

Find the equation of the perpendicular bisector of the line

joining C(-8, 5) and D(2, -3)


To find the equation of the perpendicular bisector of a line:

1. Find the midpoint of the line.

2. Find the perpendicular gradient.

3. State the equation using the midpoint and perpendicular gradient.


Some of the shapes that you can find perpendicular bisectors in:

Circle Rhombus Kite

Diagonals bisect at right angles.

Questions: Find the equations of the perpendicular bisectors of the following

1) A(2, 8) and B(4, 6) 2) Q(0, 3) and D(5, 4)

3) L(-4, 6) and M(-2, -2) 4) S(5, -7) and T(6, 4)


The perpendicular bisectors of the sides of a triangle are concurrent (intersect at a single point) and this point of intersection is called the circumcentre of the triangle.

The circumcentre is the centre of the circle which surrounds

the triangle. The three sides of the triangle are chords

in the circle.




Q1. State the equation of the line that passes through (0, 7) and is perpendicular to the line y = -1x + 2

Q2. Write in completed square form 3x2 + 12x - 2

Q3.

Q4.

L.I: Today we will be learning how to calculate the equation of an altitude in a triangle.

AltitudesAn altitude of a triangle is a line drawn from a vertex perpendicular to the opposite side. Every triangle has 3 altitudes.

Example:

The vertices of a triangle are P(5, 2) Q(-3, 0) and R(3, -4).

Find the equation of the altitude R. QP

R

Altitude

Example:

The vertices of a triangle are P(5, 2) Q(-3, 0) and R(3, -4).

Find the equation of the altitude R.Q

P

R

The 3 altitudes of a triangle are concurrent and the point of intersection is

called the orthocentre (this can also be located outside the

triangle).

Altitude

orthocentre



Q1. State the equation of the line that passes through (-1, 2) and is perpendicular to the line y = -x + 2

Q2.

Q3. State the angle that the line y = 0.5x - 3 makes with the positive direction of the x-axis

Today we will be learning about median and practising mixed questions on the straight line.

Median

A median of a triangle is a line drawn from a vertex to the mid-point of the opposite side.

Line CD is a median from C

D

mid-point of ABExample:

In the triangle ABC, find the equation of the median from B for a triangle with vertices A(-4, 1), B(-2, 4) and C(4, 1)


M

mid-point of AB

M (mid-point of BC)M (mid-point of AC)

MedianThe medians of a triangle are concurrent

and the point at which they meet is called the centroid.

Example:

In the triangle ABC, find the equation of the median from B for a triangle with vertices A(-4, 1), B(-2, 4) and C(4, 1)

Median

Pg. 20 Q10,5

Exam Questions on The Straight Line

2.

3.


Documents

S56 (5.1) Straight Line.notebook November 23, 2016missdeely.weebly.com/uploads/2/1/3/0/21307444/higher_straight_lin… · Q1. State the gradient of the line 2x + 5y = 3 Q2. State