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Presentation transcript:

© T Madas

What is the locus of a point? [plural “loci ”] It the position(s) for the point which satisfy certain conditions. (constraints) What is the locus of a point which always stays a constant distance r from another fixed point O ? The required locus is a circle r Locus O © T Madas

What is the locus of a point which is equidistant from another 2 fixed points B The required locus are the points that lie on the perpendicular bisector of AB © T Madas

What is the locus of a point which is equidistant from the sides of an angle The required locus are the points that lie on the angle bisector © T Madas

© T Madas

Find all the POINTS which are 3 cm from A B Construct the locus of the points which are equidistant from A and B © T Madas

Find all the POINTS which are 3 cm from B Construct the locus of the points which are equidistant from A and B © T Madas

Find all the POINTS which are 4 cm from A B Construct the locus of the points which are equidistant from A and B © T Madas

Find all the POINTS which are 4 cm from B Construct the locus of the points which are equidistant from A and B © T Madas

Find all the POINTS which are 5 cm from A B Construct the locus of the points which are equidistant from A and B © T Madas

Find all the POINTS which are 5 cm from B Construct the locus of the points which are equidistant from A and B © T Madas

Where do the points which are equidistant from A and B lie ? Construct the locus of the points which are equidistant from A and B © T Madas

Construct the locus of the points which are equidistant from A and B © T Madas

© T Madas

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 The diagram below shows the plan of a house using the scale 1 m = 1 cm. Using the same scale shade the locus of all the points which are within 2 m from the house. 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 4 m 7 m Use your ruler to find the points that are exactly 2 m from the top and bottom walls. © T Madas

The diagram below shows the plan of a house using the scale 1 m = 1 cm. Using the same scale shade the locus of all the points which are within 2 m from the house. 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 4 m 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 7 m Use your ruler to find the points that are exactly 2 m from the left and right walls. © T Madas

What happens at the corners? Is this correct? The diagram below shows the plan of a house using the scale 1 m = 1 cm. Using the same scale shade the locus of all the points which are within 2 m from the house. 4 m 7 m What happens at the corners? Is this correct? © T Madas

What happens at the corners? Is this correct? The diagram below shows the plan of a house using the scale 1 m = 1 cm. Using the same scale shade the locus of all the points which are within 2 m from the house. 4 m 7 m What happens at the corners? Is this correct? © T Madas

What happens at the corners? Is this correct? The diagram below shows the plan of a house using the scale 1 m = 1 cm. Using the same scale shade the locus of all the points which are within 2 m from the house. 4 m 7 m What happens at the corners? Is this correct? © T Madas

What happens at the corners? Is this correct? The diagram below shows the plan of a house using the scale 1 m = 1 cm. Using the same scale shade the locus of all the points which are within 2 m from the house. Locus 4 m 7 m What happens at the corners? Is this correct? © T Madas

© T Madas

ABCD is a rectangle with AB = 5 cm and BC = 7 cm. Find the locus of the points inside the rectangle which are within 4 cm of B and closer to AB than BC A D 5 cm Locus 45° C B 7 cm © T Madas

ABCD is a rectangle with AB = 5 cm and BC = 7 cm. Find the locus of the points inside the rectangle which are within 4 cm of B and equidistant from A and B A D 5 cm Locus C B 7 cm © T Madas

ABCD is a rectangle with AB = 5 cm and BC = 7 cm. Find the locus of the points inside the rectangle which are 4 cm from B and equidistant from A and B A D 5 cm Locus C B 7 cm © T Madas

© T Madas

AC > AB Let AB be the longer side of a triangle. What is the locus of the third vertex C, if the triangle is to be obtuse? What is the region where the 3rd point C lies, if AB is to be the longer side? C If C lied outside, then AB would not have been the longest side of the triangle in the first place. AC > AB A B © T Madas

Obtuse Let AB be the longer side of a triangle. What is the locus of the third vertex C, if the triangle is to be obtuse? What is the region where the 3rd point C lies, if AB is to be the longer side? If C lied outside, then AB would not have been the longest side of the triangle in the first place. C Let us try possible positions for the third point. A B Obtuse © T Madas

Obtuse Let AB be the longer side of a triangle. What is the locus of the third vertex C, if the triangle is to be obtuse? What is the region where the 3rd point C lies, if AB is to be the longer side? If C lied outside, then AB would not have been the longest side of the triangle in the first place. C Let us try possible positions for the third point. A B Obtuse © T Madas

Obtuse Let AB be the longer side of a triangle. What is the locus of the third vertex C, if the triangle is to be obtuse? What is the region where the 3rd point C lies, if AB is to be the longer side? If C lied outside, then AB would not have been the longest side of the triangle in the first place. C Let us try possible positions for the third point. A B Obtuse © T Madas

Obtuse Let AB be the longer side of a triangle. What is the locus of the third vertex C, if the triangle is to be obtuse? What is the region where the 3rd point C lies, if AB is to be the longer side? If C lied outside, then AB would not have been the longest side of the triangle in the first place. Let us try possible positions for the third point. C A B Obtuse © T Madas

Obtuse Where do we get acute triangles? Let AB be the longer side of a triangle. What is the locus of the third vertex C, if the triangle is to be obtuse? What is the region where the 3rd point C lies, if AB is to be the longer side? If C lied outside, then AB would not have been the longest side of the triangle in the first place. C Let us try possible positions for the third point. A B Where do we get acute triangles? Obtuse © T Madas

Acute Let AB be the longer side of a triangle. What is the locus of the third vertex C, if the triangle is to be obtuse? What is the region where the 3rd point C lies, if AB is to be the longer side? If C lied outside, then AB would not have been the longest side of the triangle in the first place. C Let us try possible positions for the third point. A B Acute © T Madas

Acute Let AB be the longer side of a triangle. What is the locus of the third vertex C, if the triangle is to be obtuse? What is the region where the 3rd point C lies, if AB is to be the longer side? If C lied outside, then AB would not have been the longest side of the triangle in the first place. C Let us try possible positions for the third point. A B Acute © T Madas

Acute Let AB be the longer side of a triangle. What is the locus of the third vertex C, if the triangle is to be obtuse? What is the region where the 3rd point C lies, if AB is to be the longer side? C If C lied outside, then AB would not have been the longest side of the triangle in the first place. Let us try possible positions for the third point. A B Acute © T Madas

Acute Let AB be the longer side of a triangle. What is the locus of the third vertex C, if the triangle is to be obtuse? What is the region where the 3rd point C lies, if AB is to be the longer side? If C lied outside, then AB would not have been the longest side of the triangle in the first place. C Let us try possible positions for the third point. A B Acute © T Madas

Let AB be the longer side of a triangle. What is the locus of the third vertex C, if the triangle is to be obtuse? It appears that you get acute triangles in the “upper” region and obtuse triangles in the “lower” region. Are the two regions separated by a straight line? Where do the right angled triangles lie? A B © T Madas

Acute Obtuse Let AB be the longer side of a triangle. What is the locus of the third vertex C, if the triangle is to be obtuse? There must be a locus where all the vertices of the right angles lie. This locus must be a “line” which divides the region into an “acute region” and an “obtuse region” Acute Obtuse What is this locus? A B © T Madas

© T Madas