problem archive
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Find the point on the x-axis which is equidistant from (2, -5) and (-2, 9). -
Find the values of y for which the distance between the points P(2, -3) and Q(10, y) is 10 units. -
If \(Q(0, 1)\) is equidistant from \(P(5, -3)\) and \(R(x, 6)\), find the values of \(x\). Also find the distances \(QR\) and \(PR\). -
Find a relation between \(x\) and \(y\) such that the point \((x, y)\) is equidistant from the point \((3, 6)\) and \((-3, 4)\). -
Draw AR, PS and BT perpendicular to the x-axis. Draw AQ and PC parallel to the x-axis. Then, by the AA similarity criterion, \[ \Delta PAQ \sim \Delta... -
If the ratio in which P divides AB is k : 1, then the coordinates of the point P will be \[ \left( \frac{k x_2 + x_1}{k + 1}, \frac{k y_2 + y_1}{k + 1... -
The mid-point of a line segment divides the line segment in the ratio 1 : 1. Therefore, the coordinates of the mid-point P of the join of the points A... -
Find the coordinates of the point which divides the line segment joining the points (4, -3) and (8, 5) in the ratio 3:1 internally. -
In what ratio does the point (-4, 6) divide the line segment joining the points A(-6, 10) and B(3, -8)? -
Find the coordinates of the points of trisection (i.e., points dividing in three equal parts) of the line segment joining the points A(2, -2) and B(-7... -
Find the ratio in which the y-axis divides the line segment joining the points (5, -6) and (-1, -4). Also find the point of intersection. -
If the points A(6, 1), B(8, 2), C(9, 4) and D(p, 3) are the vertices of a parallelogram, taken in order, find the value of p. -
Find the coordinates of the point which divides the join of \((-1, 7)\) and \((4, -3)\) in the ratio \(2 : 3\). -
Find the coordinates of the points of trisection of the line segment joining \((4, -1)\) and \((-2, -3)\). -
Find the ratio in which the line segment joining the points \((-3, 10)\) and \((6, -8)\) is divided by \((-1, 6)\). -
Find the ratio in which the line segment joining \(A(1, -5)\) and \(B(-4, 5)\) is divided by the \(x\)-axis. Also find the coordinates of the point of... -
If \((1, 2)\), \((4, y)\), \((x, 6)\) and \((3, 5)\) are the vertices of a parallelogram taken in order, find \(x\) and \(y\). -
Find the coordinates of a point \(A\), where \(AB\) is the diameter of a circle whose centre is \((2, -3)\) and \(B\) is \((1, 4)\). -
If \(A\) and \(B\) are \((-2, -2)\) and \((2, -4)\), respectively, find the coordinates of \(P\) such that \(AP = \frac{3}{7} AB\) and \(P\) lies on t... -
Find the coordinates of the points which divide the line segment joining \(A(-2, 2)\) and \(B(2, 8)\) into four equal parts.