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Equation of a line parallel to y-axis:
Let LM be a straight line parallel to y-axis at a distance k from the y-axis. Then, the abscissa (the x-coordinate), x=k. Hence, the equation of the line parallel to y-axis is x = k. ..
Rectangular co - ordinates
The position of the point P in a plane in the rectangular co-ordinate system is determined as follows: Draw PA and PB perpendicular to XX' and YY'. The segment OA = a measures the distance along the x-axis (the x-coordinate and the perpendicular distance AP = OB = b ( parallel to y - a..
Applications of Definite Integrals
Let y = f (x) be a curve. The area bounded by y = f (x), x-axis and the ordinates at x = a and x = b is given byLet y = f (x) be a curve. The area bounded by y = f (x), x-axis and the ordinates at x = a and x = b is given by (ii) The area bounded by the curve..
Question 9
image Question: Calculate the distance between A (7, 3) and B on the x-axis whose abscissa is 11. [2 Mark] Answer: The co-ordinates of B are (11, 0). (on the x-axis, y = 0, abscissa = x-coordinate = 11)..
Note:
i) If the points A and B lie on the x-axis, then the ordinates of A and B are zeros. i.e., A (x 1 , 0), B (x 2 ,0) ii) If the points A and B lie on the y-axis, then the abscissae of A and B are zeros. i.e., A (0,y 1 ) and B (0,y 2 ) iii) Distance of any ..
Ordered Pairs and Cartesian Product
In a Rectangular Cartesian System of coordinates the position of a point in a plane is determined by an ordered pair whose elements give the distances from the intersecting straight lines at right angles to each other. These lines are called the axes. The vertical line is called the Y-a..
Question 10
image Question: A point A is at a distance from the point (4, 3). Find the co-ordinates of point A, if its ordinate is twice of its abscissa. [3 Mark] Answer: Ordinate is y-co-ordinate and Abscissa is x co-ordinate. Let the co-ordinates of A be (x, y..
Translation of Axes
. Let O'X' and O'Y' be new axes parallel to OX and OY, respectively, where O' is the new origin. Let (h,k) be the coordinates of O' referred to the old axes, i.e., OL = h and LO' = k. Also, OM = x and MP = y . Let O'M' = x' and M'P = y' be respectively, the abscis..
Rectangular coordinate system
The position of a point in a plane is determined by two coordinates. The method is as follows: Two mutually perpendicular lines (straight lines) XX' and YY' are drawn as shown in the figure. These straight lines are termed as coordinate axes, the one (usually drawn horizontally) is called the x-axi..
Rectangular coordinate system
Rectangular coordinate system - The position of a point in a plane is determined by two coordinates. The method is as follows: Two mutually perpendicular lines (straight lines) XX' and YY' are drawn as shown in the figure. These straight lines are termed as coordinate axes, the one (usually drawn h..
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