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प्रश्न
Use a graph sheet for this question, take 2 cm = 1 unit along both x and y-axis:
- Plot the points A (3, 2) and B (5, 0). Reflect point A on the y-axis to A΄. Write co-ordinates of A΄.
- Reflect point B on the line AA΄ to B΄. Write the co-ordinates of B΄.
- Name the closed figure A’B’AB.
उत्तर
(a) A' (- 3, 2)
(b) Since we know that,
The reflection of point (a, b) with respect to line y = k is a point (a, 2k- b)
Here, k = 2, a = 5, b = 0
∴ B' = (5, 2 × 2 - 0)
∴ B' = (5, 4)
(c) A'B'AB is an arrowhead
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संबंधित प्रश्न
Use graph paper for this question (Take 2 cm = 1 unit along both x and y-axis). ABCD is a quadrilateral whose vertices are A(2, 2), B(2, –2), C(0, –1) and D(0, 1).
1) Reflect quadrilateral ABCD on the y-axis and name it as A'B'CD
2) Write down the coordinates of A' and B'.
3) Name two points which are invariant under the above reflection
4) Name the polygon A'B'CD
Three vertices of parallelogram ABCD taken in order are A(3, 6), B(5, 10) and C(3, 2)
1) the coordinate of the fourth vertex D
2) length of diagonal BD
3) equation of the side AD of the parallelogram ABCD
Using a graph paper, plot the points A(6, 4) and B(0, 4).
- Reflect A and B in the origin to get the images A' and B'.
- Write the co-ordinates of A' and B'.
- State the geometrical name for the figure ABA'B'.
- Find its perimeter.
A straight line passes through the points P(–1, 4) and Q(5, –2). It intersects the co-ordinate axes at points A and B. M is the mid-point of the segment AB. Find:
- The equation of the line.
- The co-ordinates of A and B.
- The co-ordinates of M.
A line through origin meets the line x = 3y + 2 at right angles at point X. Find the co-ordinates of X.
O(0, 0), A(3, 5) and B(−5, −3) are the vertices of triangle OAB. Find the equation of median of triangle OAB through vertex O.
P(3, 4), Q(7, –2) and R(–2, –1) are the vertices of triangle PQR. Write down the equation of the median of the triangle through R.
Point A and B have co-ordinates (7, −3) and (1, 9) respectively. Find:
- the slope of AB.
- the equation of perpendicular bisector of the line segment AB.
- the value of ‘p’ of (−2, p) lies on it.
Use a graph sheet for this question.
Take 1 cm = 1 unit along both x and y axis.
(i) Plot the following points:
A(0,5), B(3,0), C(1,0) and D(1,–5)
(ii) Reflect the points B, C and D on the y axis and name them as B',C'andD' respectively.
(iii) Write down the coordinates of B',C 'and D'
(iv) Join the point A, B, C, D, D ', C ', B', A in order and give a name to the closed figure ABCDD'C'B
A line is of length 10 units and one end is at the point (2, – 3). If the abscissa of the other end be 10, prove that its ordinate must be 3 or – 9.
