Chapter 5 slides

​Chapter 5 : Locus & Straight lines

Locus

A set of points in a plane which satisfy certain geometrical condition (or conditions) is called a locus.

L = {P | P is a point in a plane and P satisfy given geometrical condition} Here P is the representative of all points in L.

The circle with center O and radius 4 is the set L = { P | OP = 4, P is a point in the plane }

Set of points on a circle

The perpendicular bisector of segment AB is the set M = { P | P is a point in a plane such that PA = PB }.

Perpendicular bisector

Examples:

Multiple Choice

The equation y = 0 represents what in the xy-plane?

• y-axis

• x-axis

• origin

• None of the above

Multiple Choice

L = {P | P is a point in the xy-plane which is 3 units away from (2, -3)}.

The locus L above represents which of the following below?

• Rectangle

• Square

• Triangle

• Circle

Fill in the Blanks

If the origin is shifted to the point O'(3,2) the directions of the axes remaining the same, find the new co-ordinates of the point (10, -5) and add the new x and y coordinates. Write the result as a number below.

Fill in the Blanks

If the co-ordinates (5,14) change to (8,3) by shift of origin, find the coordinates of the new origin and add them together. Write the result as a number below?

​Some important pointers about slope.

Multiple Choice

A line has its x-intercept to be a and -a respectively. What can you say about the slope of the line if it is given that a is negative?

• Slope is 0.

• Slope is undefined.

• Slope is positive.

• Slope is negative.

General form of a line:

ax + by = c

Slope intercept form of a line: y = mx + c

Point-slope form of a line: y - y₁ = m (x - x₁)

Two point form of a line:
(y - y₁) ∕ (x - x₁)= (y₂ - y₁ ) ∕ (x₂ - x₁)

Double-intercept form of a line:
x ∕ a + y ∕ b = 1

xcosα + ysinα = p

Normal form of a line:

Multiple Choice

Decide whether the line 2x − 4y = 5 and 2x + y = 17 are perpendicular to each other.

• Yes

• No

• Cannot decide

• None of the above.

Fill in the Blanks

Figure out the equation of a line which has a slope of 3 and has an x-intercecpt of 3.

After that, write the equation in the general form and figure out the value of a*b.

Multiple Choice

Find the equation of the line which is parallel to the line 3x + y = 5 and passes through the origin.

• y = -5x

• y = (1/3x)

• y = 3x

• y = -3x