Coordinate geometry
The Basics:
Find the distance between two points using Pythagoras' theorem. The midpoint is the average (mean) of the coordinates.
The gradient =
Parallel lines have the same gradient. The gradients of perpendicular lines have a product of -1. Straight Lines:
Equation of a straight line is y = mx + c, where m = gradient, c = y-intercept. The equation of a line, if we know one point and the gradient is found using: (y - y1) = m(x - x1)
(If given two points, find the gradient first, and then use the formula.) Two lines meet at the solution to their simultaneous equations. Note: When a line meets a curve there will be 0, 1, or two solutions. 1. Use substitution to solve the simultaneous equations

2. Rearrange them to form a quadratic equation
3. Solve the quadratic by factorising, or by using the quadratic formula. 4. Find the y-coordinates by substituting these values into the original equations. Other Graphs (also in Functions):

Sketch the curve by finding:
1. Where the graph crosses the y-axis.
2. Where the graph crosses the x-axis.
3. Where the stationary points are.
4. Whether there are any discontinuities.
5. What happens as
Circles:
Cartesian equation for a circle is (x - a)2 + (y - b)2 = r2 , where (a, b) is the centre of the circle and r is the radius. Parametric Equations:
Sketch the graph by substituting in values and plotting points. Find the cartesian form by either using substitution (use t = ...), or by using the identity, . Find the gradient using the chain rule:

...with radicals are discussed. At the end of this unit the student will be in a position to apply the acquired knowledge in algebraic problems that model various situations.
Seventh unit: equations and inequalities. In this unit, methods for solving equations and inequalities are studied. Problems as an equation or an inequality of first or second degree with one variable are resolved, pretending that the students infer that there are situations in...

...Analyticgeometry, or analytical geometry, has two different meanings in mathematics. The modern and advanced meaning refers to the geometry of analytic varieties. This article focuses on the classical and elementary meaning.
In classical mathematics, analyticgeometry, also known as coordinate geometry, or Cartesian geometry, is the study of geometry...

...Straight Lines, Pair of Lines & Circles A straight line through the point A 3, 4 is such that its intercept between the axes is bisected at
A . It’s equation is
1.
(a) 4 x 3 y 24 Ans: a
(b) 3x 4 y 25
(c) x y 7
(d) 3x 4 y 7 0
Sol: By formula required equation is given by
x y 2 4 x 3 y 24 3 4
2. The equation of the line which is the perpendicular bisector of the line joining the points 3, 5 and...

...questions 13-14:
y = x – 3
13. Test the equation for symmetry with respect to the x-axis, the y-axis, and the origin.
A) Symmetric with respect to the x-axis
B) Symmetric with respect to the y-axis
C) Symmetric with respect to the origin
D) No symmetry with respect to x-axis, y-axis, or origin
Ans: D Section: 2.1
14. Sketch the graph of the equation.
A) C)
B) D)
Ans: A Section: 2.1
15. Test the...

...C OORDINATE GEOMETRY
COORDINATE GEOMETRY
155
7
7.1 Introduction
In Class IX, you have studied that to locate the position of a point on a plane, we
require a pair of coordinate axes. The distance of a point from the y-axis is called its
x-coordinate, or abscissa. The distance of a point from the x-axis is called its
y-coordinate, or ordinate. The coordinates of a point on the x-axis are of the form
(x, 0), and of a point on the y-axis are of the form (0, y)....

...k
g
l = (1)
Here k is the spring constant and g is the acceleration due to gravity.
Equation (1) is and equation of straight line slope of this line is given by-
Slope =
k
g
=> k =
slope
g...

...operations.
2. SOCIAL(Social Media Analytics)
Online social networks bleed information. Every time someone posts something on Twitter, Facebook, or Pinterest, they create a digital footprint. Every time someone else reads it, or watches a YouTube video, they add to the data trail. Facebook is currently building a data centre in Sweden the size of 11 football fields, joining two others in America, just to collect and process the stuff.
Social media...

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