Hi, I'm Teacher Daisy. Now, let's learn Form 3 Chapter 8 Loci in 2 Dimension. In this chapter, you will learn 8.1, Locus.
8.2, Loci in 2 Dimensions. 8.1, Locus. A locus is a trace or trajectory, formed by a set of points in a plane or three-dimensional space, that satisfies certain conditions.
The shapes of two-dimensional loci, can be seen in the form of straight lines, arcs and curves. Example A, point C is drawn on a blade of a revolving fan. Elaborate and sketch the locus of point C. Solution, this lotus is a circle.
Example B, point C on a swinging pendulum. Solution, a curve. Example C, the diagram shows a pole MN. A rectangular board PQRS is attached to the pole where PQRS is movable.
If the side PQ is rotated 360 degree around MN, what is the three-dimensional shape formed? Solution, the shape formed when the side PQ is rotated 360 degree around pole MN is a right cylinder. Example D, the diagram shows a pole MN.
A semicircular board PQR is attached to the pole where PQR is movable. If PQR is rotated 360 degree around MN, what is the three-dimensional shape formed? Solution The shape formed when the semicircular board is rotated 360 degree around pole MN is a sphere.
8.2 loci in two dimensions In general, there are five points. 1. The locus of a point that is equidistant from a fixed point, is a circle centered at that fixed point. Example, construct a locus of point P which is always 3 cm from a fixed point O.
Mark point O. Set the gap of the compass at 3 cm. Construct a circle of radius 3 cm centered at the point O.
2. The locus of a point, that is equidistant from two fixed points, is the perpendicular bisector of the line, connecting the two fixed points. Example, construct the locus of point P, that is equidistant from two fixed points, M and N. Mark two small arcs, using a pair of compasses, with the gap set at more than half of the length of MN, from the point M.
With the compasses set at the same gap, mark the intersecting arcs of point M. Connect the two points of intersection, with a straight line. 3. The locus of points that are of constant distance, from a straight line. are straight lines parallel to that straight line.
Example, the diagram shows a line AB drawn on a square grid with sides of one unit. Draw the locus of point P, which always moves at three units from the line AB. Solution, the locus of point P moving three units from the line AB is a pair of lines parallel to AB. and 3 units from AB. 4. The locus of points that are equidistant from two parallel lines is a straight line parallel to and passes through the midpoints of a pair of parallel lines.
Example, the diagram shows the rectangle ABCD. Draw the locus of P, which is equidistant from the lines AB and DC. Solution, the locus of point P, that is equidistant from the line A, B and D, C, is a line parallel to A, B and D, C, and is 3 units, from the lines A, B and D, C.
5. The locus of points that are equidistant from, two intersecting lines, is the angle by sector, of the angles formed by the intersecting lines. Example, construct the locus of point P, that is equidistant from two straight lines, PQ and PN, intersecting at P. By using a pair of compasses, draw an arc from the point P, which cuts through the straight lines. PQ and PN. Mark the points of intersection, between the arc, and the straight lines, PQ and PN, as A1 and A2 respectively.
Construct intersecting mark from A1 and A2. Draw a straight line joining the intersecting mark constructed, and the point P. Determine locus that satisfies two or more conditions. Example, point X and Y are two points, that move inside the square ABCD.
On the grid. 1. Draw the locus of a moving point X, which is constantly 7 units from A. 2. Draw the locus of a moving point Y, which is equidistant from the lines, AB and CD. 3. Mark all points of intersection of locus of X, and locus of Y, with a symbol. Lastly, the Chapter 8 concept map is shown as below.
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