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Coordinate Geometry Class Tenth

Subject: Mathematics
Find the ratio in which the point (-3,p) divides the line segment joining the points (-5, -4) and (-2,3). Also find the value of p.(3)
Determine the ration in which the line 3x + y – 9 = 0 divides the segment joining the pt (1,3) and (2,7).(3)
Find the value of x if the distance between the points (x, 1) and (3,2) is 5. (3)
If the mid points of sides of the triangle are (2,6), (6.4) and (4,2) find its vertices.(5)
The coordinates of the mid-point of the line joining the points (3p, 4) and (-2, 2q) are (5, p). Find the values of p and q.
Find the ratio in which the line-segment joining the points (6, 4) and (1, -7) is divided by x-axis.
Find the value of m for which the points with coordinates (3, 5), (m, 6) and are collinear.
Find the value of k for which the points with coordinates (3, 2), (4, k) and (5, 3) are collinear.
If the point P(x, y) is equidistant from the points A (5, 1) and B (-1, 5), prove that 3x - 2y = 0(5)
The line joining the points (2, 1) and (5, -8) is trisected at the points P and Q. If point P lies on the line 2x - y + k = 0, find the value of k.(5)
The vertices of a triangle are A(3,4), B(7,2) and C(-2, -5).Find the length of the median through the vertex B.
The co-ordinates of one end of the diameter of a circle are (3,5) and the co-ordinates of its center are (7,4). Find out the co-ordinates of the other end of the diameter
Prove that the points (3, 0), (6, 4) and (-1, 3) are vertices of a right-angled triangle. Also, prove that these are the vertices of an isosceles triangle.
If (-2, -1); (a, 0); (4, b) and (1, 2) are the vertices of a parallelogram, find the values of a and b.
If the distance of P (x, y) from A (6,3) and B (-3,6) are equal prove that 3x = y.
If the pt A(-2, -1) B(1, 0) C(x, 3) and D(1, y) lie on the ends of parallelogram find the value of X and y.
Find the coordinates of point’s which trisect the line segment joining (1 , 2 ) and (-3 , 4 ).
The area of a triangle is 5.Two of it’s vertices are (2,1) and (3, -2). The third vertex lies on y = x + 3.find the third vertex.(5)

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