1 / 29

Term 3 : Unit 2 Coordinate Geometry

Term 3 : Unit 2 Coordinate Geometry. Name : _____________ ( ) Class : ________ Date : ________. 2.1 Midpoint of the Line Joining Two Points. 2.2 Areas of Triangles and Quadrilaterals. 2.3 Parallel and Non-Parallel Lines. 2.4 Perpendicular Lines. 2.5 Circles. Coordinate Geometry.

collier
Download Presentation

Term 3 : Unit 2 Coordinate Geometry

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Term 3 : Unit 2Coordinate Geometry Name : _____________ ( ) Class : ________ Date : ________ 2.1 Midpoint of the Line Joining Two Points 2.2 Areas of Triangles and Quadrilaterals 2.3 Parallel and Non-Parallel Lines 2.4 Perpendicular Lines 2.5 Circles

  2. Coordinate Geometry 2.1 Midpoint of the Line Joining Two Points Objectives In this lesson, you will learn how to find the midpoint of a line segment and apply it to solve problems.

  3. D is and E is M is the point Coordinate Geometry A line AB joins points (x1, y1) and (x2, y2). M (x, y) is the midpoint of AB. Take the x-coordinate of D and the y-coordinate of E. Construct a right angled triangle ABC. Construct the midpoints D and E of the line segments AC and BC. Take the mean of the coordinates at the endpoints.

  4. Coordinate Geometry Example 1 P, Q, R and S are coordinates of a parallelogram and M is the midpoint of PR. Find the coordinates of M and S and show that PQRS is a rhombus. M is also the midpoint of QS.

  5. Coordinate Geometry Example 2 3 points have coordinates A(–1, 6), B(3, 2) and C(–5, –4). Given that D and E are the midpoints of AB and AC respectively, calculate the midpoint and length of DE. Let M be the midpoint of DE.

  6. Coordinate Geometry Example 3 If A(2, 0), B(p, –2), C(–1, 1) and D(3, r) are the vertices of a parallelogram ABCD, calculate the values of p and r. Let M be the midpoint of AC. M is also the midpoint of BD.

  7. Coordinate Geometry 2.2 Areas of Triangles and Quadrilaterals Objectives In this lesson, you will learn how to find the areas of rectilinear figures given their vertices.

  8. Coordinate Geometry Area of Triangles ABC is a triangle. We will find its area. Construct points D and E so that ADEC is a trapezium.

  9. Coordinate Geometry ABC is a triangle. The vertices are arranged in an anticlockwise direction. We will find its area. Construct points D, E and F on the x-axis as shown.

  10. Coordinate Geometry Definition From the previous slide, we know that

  11. Coordinate Geometry Example 4 Find the area of a triangle with vertices A(–2, –1), B(2, –3) and C(4, 3). The vertices A, B and C follow an anticlockwise direction.

  12. Coordinate Geometry Area of Quadrilaterals Find the area of a quadrilateral with vertices A(x1, y1 ), B(x2, y2 ), C(x3, y3 ) and D(x4, y4 ), following an anticlockwise direction. Split the quadrilateral into two triangles.

  13. Coordinate Geometry The area of a quadrilateral with vertices A(x1, y1 ), B(x2, y2 ), C(x3, y3 ) and D(x4, y4 ), following an anticlockwise direction. The method for finding the area of quadrilaterals is very similar to that of triangles.

  14. Coordinate Geometry Example 5 Find the area of a quadrilateral with vertices P(1, 4), Q(–4, 3), R(1, –2) and S(4, 0), following an anticlockwise direction.

  15. Coordinate Geometry 3.3 Parallel and Non-Parallel Lines Objectives In this lesson, you will learn how to apply the conditions for the gradients of parallel lines to solve problems.

  16. Coordinate Geometry Consider the straight line with equation y = m1 x + c1 that makes an angle of θ1 with the positive x-axis. Translate the line parallel to the x-axis. The new line has equation y = m2 x + c2 and makes an angle of θ2 with the positive x-axis. The lines are parallel to each other. θ1 = θ2 The lines make the same angle with the x-axis. m1 = m2 The lines have the same gradient.

  17. Coordinate Geometry Example 6(a) The diagram shows a parallelogram ABCD with A and C on the x-axis and y-axis respectively. The equation of AB is x + y = 2 and the equation of BC is 2y = x + 10. (a) Find the coordinates of A, B and C.

  18. Coordinate Geometry Example 6(b) The diagram shows a parallelogram ABCD with A and C on the x-axis and y-axis respectively. The equation of AB is x + y = 2 and the equation of BC is 2y = x + 10. (b) Find the equations of AD and CD. AD is parallel to BC (2y = x + 10). CD is parallel to AB (x + y = 2 ). Gradient of AD = gradient of BC = 0.5 Gradient of CD = gradient of AB = –1 Since A is (2, 0) Since C is (0, 5)

  19. Coordinate Geometry Example 7 Find the equation of the line which passes through the point (–2, 3) and is parallel to the line 2x + 3y – 3 = 0. m in y = mx + c is the gradient of the line. Rearrange in the form y = mx + c.

  20. Coordinate Geometry 2.4 Perpendicular Lines Objectives In this lesson, you will learn how to apply the conditions for the gradients of perpendicular lines to solve problems.

  21. Coordinate Geometry Consider the straight line with equation y = m1 x + c1 that makes an angle of θ1 with the positive x-axis. Rotate the line clockwise through 90°. The new line has equation y = m2 x + c2 and makes an angle of θ2 with the negative x-axis. Applies to any two perpendicular lines.

  22. Coordinate Geometry Example 8 Two points have coordinates A(–2, 3) and B(4, 15). Find the equation of the perpendicular bisector of AB. Hence calculate the coordinates of the point P on the line 3y = x + 1 if P is equidistant from A and B. Solve simultaneous equations Find P. Adding the equations Substitute for y

  23. Coordinate Geometry Example 9 The points A and B have coordinates (5, 2) and (3, 6) respectively. P and Q are points on the x-axis and y-axis and both P and Q are equidistant from A and B. • Find the equation of the perpendicular bisector of AB. (b) Find the coordinates of P and Q.

  24. Curves and Circles 2.5 Circles Objectives • In this lesson, you will learn to • recognise the equation of a circle, • find the centre and radius of a circle, • find the intersection of a circle and a straight line.

  25. Curves and Circles Consider the point C(a, b) and a point P(x, y). The distance between C and P is The locus of P as the line rotates around C is a circle of radius r. The equation of the circle is

  26. Curves and Circles The circle with centre C(a, b) and radius r has equation The general form of the equation is

  27. Curves and Circles Example 10 Find the equation of the circle whose centre is C(–3, 4) and which touches the x–axis. The radius of the circle is 4 units. The equation of the circle is: The radius is the y-coordinate of C.

  28. Curves and Circles Example 11 Find the coordinates of the points of intersection of the line 2y + x = 12 with the circle x2 + y2 – 6x – 4y – 12 = 0. Substitute for x into the circle equation. Using x = 12 – 2y. The points are

  29. Curves and Circles Example 12 (a) Give the equation of the circle with centre C(–2, 0) and radius r = 3. The equation is (b) Find the coordinates of the centre and the radius of the circle x2 + y2 – 2x – 6y + 1 = 0.

More Related