Shortcuts video on Coordinate geometry

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Scope of Coordinate Geometry
Coordinate geometry is one of the most important and exciting ideas of mathematics. In particular it is central to the mathematics students meet at school. It provides a connection between algebra and geometry through graphs of lines and curves.

  • Distance btw points
  • Midpoint btw points
  • Slopes
  • Slope of parallel lines
  • Slope of Perpendicular lines
  • Shape of figure formed by points
  • Area

 Importance in Exams

Coordinate Geometry in CAT – 1 ques
Coordinate Geometry in SNAP – 1 ques
Coordinate Geometry in CMAT – 2 ques
Coordinate Geometry in NMAT – 5 to 7 ques

Questions based on Coordinate geometry..
(Cetking students can solve all these questions without using pen! or any formula)

1. Find the midpoint of the segment joining the points (4, -2) and (-8,6).
[1] (6, 4) [2] (-6,-4) [3] (2, 2) [4] (-2, 2)

2. Find the distance between the points (3, -2) and (6,4).
[1] V85 [2] V79 [3] 5V3 [4] 3V3

3. What is the slope of the line passing through the points (4,6) and (-1,-2)?
[1] 4/3 [2] 3/4 [3] 8/5 [4] 5/8

4. M is the midpoint of . The coordinates of A are (-2,3) and the coordinates of M are (1,0).
Find the coordinates of B.
[1] (-1/2, 3/2) [2] (4,-3) [3] (-4,3) [4] (-5,6)

5. Find the equation of the line parallel to the line whose equation is y = 6x + 7 and whose
y-intercept is 8.
[1] y = -6x + 8 [2] y = (-1/6)x + 8 [3] y = (1/6)x + 8 [4] y = 6x + 8

6. When proving that a triangle is a right triangle using coordinate geometry methods, you must:

[1] show that the slopes of two of the sides are negative reciprocals creating perpendicular lines and right angles.
[2] show that the lengths of the sides satisfy the Pythagorean Theorem, thus creating a right angle.
[3] both choices 1 and 2 may be used.
[4] neither choice 1 nor 2 may be used.

7. Which point satisfies the linear quadratic system y = x + 3 and y = 5 – x2?
[1] (-2,1) [2] (2,1) [3] (-1,2) [4] (4,-1)

8. When proving that a quadrilateral is a trapezoid, it is necessary to show
[1] only one set of parallel sides.
[2] one set of parallel sides and one set of non-parallel sides.
[3] one set of parallel sides and one set of congruent sides.
[4] two sets of parallel sides.

9. Find the slope of a line perpendicular to the line whose equation is 2y + 6x = 24.
[1] -3 [2] 6 [3] 1/3 [4] -1/6

10. A student enters the following information into his/her calculator when attempting to find the slope between the points (6,7) and (-5,3). Which of the following statements is TRUE?
[1] The student is correct, the slope is 11.5.
[2] The slope formula does not involve subtraction.
[3] The slope is actually -11.5.
[4] The slope is actually 4/11.

11. Find the midpoint of the segment connecting the points (a, b) and (5a, -7b).
[1] (3a, -3b) [2] (2a, -3b) [3] (3a, -4b) [4] (-2a, 4b)

Coordinate Geometry in CAT – 1 ques
Coordinate Geometry in SNAP – 1 ques
Coordinate Geometry in CMAT – 2 ques
Coordinate Geometry in NMAT – 5 to 7 ques

Solution
1-4
2- 5v3
3-3
4-2
5-4
6-2
7-1
8-3
9-3
10-4
11-1

Scope of Coordinate Geometry and formulas:

Graph Transformations

  • Horizontal Shifting. An applet helps you explore the horizontal shift of the graph of a function.
  • Vertical Shifting. An applet that allows you to explore interactively the vertical shifting or translation of the graph of a function.
  • Horizontal Stretching and Compression. This applet helps you explore the changes that occur to the graph of a function when its independent variable x is multiplied by a positive constant a (horizontal stretching or compression).
  • Vertical Stretching and Compression. This applet helps you explore, interactively, and understand the stretching and compression of the graph of a function when this function is multiplied by a constant a.
  • Reflection of Graphs In x-axis. This is an applet to explore the reflection of graphs in the x-axis by comparing the graphs of f(x) (in blue) and h(x) = -f(x) (in red).
  • Reflection of Graphs In y-axis. This is an applet to explore the reflection of graphs in the y-axis by comparing the graphs of f(x)(in blue) and h(x) = f(-x) (in red).
  • Reflection Of Graphs Of Functions. This is an applet to explore the reflection of graphs in the y axis and x axes. Graphs of f(x), f(-x), -f(-x) and -f(x) are compared and discussed.

Equation of Line

  • Slope of a Line. The slope of a straight line, parallel and perpendicular lines are all explored interactively using an applet.
  • General Equation of a Line: ax + by = c. Explore the graph of the general linear equation in two variables that has the form ax + by = c using an applet.
  • Slope Intercept Form Of The Equation Of a Line. The slope intercept form of the equation of a line is explored interactively using an applet. The investigation is carried out by changing parameters m and b in the equation of a line given by y = mx + b.
  • Find Equation of a Line – applet. An applet that generates two lines. One in blue that you can control by changing parameters m (slope) and b (y-intercept). The second line is the red one and it is generated randomly. As an exercise, you need to find an equation to the red line of the slope intercept form y = mx + b.

Equation of Parabola

  • Construct a Parabola. An applet to construct a parabola from its definition.
  • Equation of Parabola. An applet to explore the equation of a parabola and its properties. The equation used is the standard equation that has the form (y – k) 2 = 4a(x – h)
  • Find Equation of Parabola – applet. An applet that generates two graphs of parabolas. As an exercise, you need to find an equation to the red parabola.

Equation of Circle

  • Equation of a Circle. An applet to explore the equation of a circle and the properties of the circle. The equation used is the standard equation that has the form (x – h) 2 + (y – k) 2 = r 2.
  • Find Equation of Circle – applet. This is an applet that generates two graphs of circles. The equations of these circles are of the form (x – h) 2+ (y – k) 2 = r 2. You can control the parameters of the blue circle by changing parameters h, k and r. The second circle is the red one and it is generated randomly. As an exercise, you need to find an equation to the red circle.

Equation of Ellipse

  • Equation of an Ellipse. This is an applet to explore the properties of the ellipse given by the following equation (x – h) 2 / a 2 + (y – k) 2 / b 2 = 1.

Equation of Hyperbola

  • Equation of Hyperbola. The equation and properties of a hyperbola are explored interactively using an applet. The equation used has the form x 2/a 2 – y 2/b 2 = 1 where a and b are positive real numbers.

Systems Of Equations

  • Systems of Linear Equations – Graphical Approach. This large window java applet helps you explore the solutions of 2 by 2 systems of linear equations.

Polar Coordinates And Equations

  • Polar Coordinates and Equations. The graphs of some specific polar equations are explored using java applet. You can also plot your own points generated using the polar equation under investigation.

Polynomials

  • Multiplicity of Zeros and Graphs of Polynomials. A large screen applet helps you explore the effects of multiplicities of zeros on the graphs of polynomials the form f(x) = a(x-z1)(x-z2)(x-z3)(x-z4)(x-z5).
  • Polynomial Functions. This page contains a large window java applet to help you explore polynomials of degrees up to 5 : f(x) = ax5 + bx4 + cx3 + dx2 + ex + f.
  • Third Degree Polynomials – Applet. A large screen applet helps you explore graphical properties of third order polynomials of the form: f(x) = ax3 + bx + c.
  • Fourth Degree Polynomials – Applet. Use an applet to explore graphical properties of fourth degree polynomials of the form: f(x) = ax4 + bx2 + c.

Matrix Multiplication

  • The Process of Matrix Multiplication . This applet helps you explore the definition and process of multiplying matrices.

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