An Important Question of class 10 Based on Section Formula Chapter of M.L Aggarwal for ICSE BOARD.
Here you have point some co-ordinates on the graph as required in question So solve this question.
This is the Question Number 08, Exercise 11 of M.L Aggarwal.
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Use graph paper for this question. Take 1 cm = 1 unit on both axes. Plot the points A(3, 0) and B(0, 4). (i) Write down the co-ordinates of A1, the reflection of A in the y-axis. (ii) Write down the co-ordinates of B1, the reflection of B in the x-axis. (iii) Assign the special name to the quadrilateral ABA1B1. (iv) If C is the midpoint is AB. Write down the co-ordinates of the point C1, the reflection of C in the origin. (v) Assign the special name to quadrilateral ABC1B1.
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(i) Co-ordinates of point A are (3,0).
When you reflect a point across the Y-axis, the y-coordinate remains the same,
but the x-coordinate is transformed into its opposite (its sign is changed)
Hence the reflection of A in the Y axis is (-3,0).
(ii) Co-ordinates of point B are (0,4).
When you reflect a point across the X-axis, the x-coordinate remains the same,
but the y-coordinate is transformed into its opposite (its sign is changed).
Hence the reflection of B in the X-axis is (0,-4)
(iii) The quadrilateral ABA1B1 will be a rhombus.
(iv) Let C be midpoint of AB.
Co-ordinate of C = ((3+0)/2 , (0+4)/2) = (3/2, 2) [Midpoint formula]
In a point reflection in the origin, the image of the point (x,y) is the point (-x,-y).
Hence the reflection of C in the origin is (-3/2, -2)
(v) In quadrilateral ABC1B1, ABB1C1
Hence the quadrilateral ABC1B1 is a trapezium.