**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) = ax
^{5}+ bx^{4}+ cx^{3}+ dx^{2}+ ex + f. - Third Degree Polynomials – Applet. A large screen applet helps you explore graphical properties of third order polynomials of the form: f(x) = ax
^{3}+ bx + c. - Fourth Degree Polynomials – Applet. Use an applet to explore graphical properties of fourth degree polynomials of the form: f(x) = ax
^{4}+ bx^{2}+ c.

**Matrix Multiplication**

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