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Find the distance between the points \(a(\cos35^o,0)\ \text{and}\ (0,a \cos 55^o) \)
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Find the value of x which is an integer such that the distance between the points P(x, 2) and Q(3, – 6) is 10 units.
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Is the point (4, 4) equidistant from the points P(–1, 4) and Q(1, 0)?
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ie A is equidistant from B and C
A is a point on the xaxis and B is a point on the yaxis. If the abscissa of A be a and the ordinate of B be –a, then find the length of segment AB.
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Coordinate of
Coordinate of
What is the distance between A on the xaxis whose abscissa is 11 and B(7, 3)?
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Find the coordinates of the other end of a diameter of a circle whose one end is \(A(2, 1)\) and centre is \(P\left(\dfrac{3}{2},\dfrac{5}{2}\right) \).
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Coordinates of
Find the coordinates of the centroid of the triangle whose vertices are (0, 6), (8, 12) and (8, 0).
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If the point (a, b) is equidistant from the points (7, 1) and (3, 5), find the relation between a and b.
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Two vertices of a triangle are A (–7, 4) and B (3, –5). If its centroid is (2, –1), then find the coordinates of the third vertex C.
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The mid–point of the line segment joining (3, 6) and (x, 2) is (2, y). Find the values of x and y.
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What point on the x–axis is equidistant from (7, 6) and (–3, 4) ?
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Point on xaxis
A/Q
The point
Find the ratio in which the line segment joining the points (6, 4) and (1, –7) is divided by the x–axis.
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But
Find the distance between the points A(x + y, x – y) and B(x – y, – x – y).
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Are the points A(a, b + c), B(b, c + a) and C(c, a + b) collinear ?
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The given points are collinear
Find the value of x if the points (x, 8), (– 4, 2) and (5, –1) are collinear.
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Is \(\triangle \) ABC with vertices A(– 2, 0), B(2, 0), C(0, 2) similar to \(\triangle \) DEF with vertices D(– 4, 0), E(0, 4) and F(4, 0) ? Justify your answer.
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Find the points on the yaxis, each of which is at a distance of 13 units from the point (–5, 7).
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Let the point be (0, 4)
Point is (0, 19), (0, 5)
Are the points A(4, 5), B(7, 6) and C(6, 3) collinear?
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It is not collinear as area is not equal to 0
If the points P(a, –11), Q(5, b), R(2, 15) and S(1, 1) are the vertices of a parallelogram PQRS, find the values of a and b.
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Mid point of Mid point of
and
Find all possible values of a for which the distance between the points A(a, –1) and B(5, 3) is 5 units.
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Show that the points A(3, 1), B(12, –2) and C(0, 2) cannot be the vertices of a triangle.
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Area
So the points are collinear and it cannot be the vertex of a
If the points A(– 6, 10), B(– 4, 6) and C(3, –8) are collinear, then show that \(AB=\dfrac{2}{9}AC \).
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Area
So points are collinear
Find the coordinates of the point R which divides the line segment joining the points P(–2, 3) and Q(4, 7) internally in the ratio 4 : 7.
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coordinates of
If the point C(–1, 2) divides internally the line segment joining A(2, 5) and B in the ratio 3 : 4, find the coordinates of B.
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Check whether the point P(–2, 4) lies on a circle of radius 6 units and centre C(3, 5).
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Distance of
which is not equal to the radius. Hence it does not lie on the circle
Does the point A(– 4, 2) lie on the line segment joining the points X(– 4, 6) and Y(– 4, –6) ? Justify your answer.
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In what ratio does the point P(2, –5) divide the line segment joining A(– 3, 5) and B(4, –9) ?
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Show that the points A(–1, –2), B(4, 3), C(2, 5) and D(–3, 0) are the vertices of the rectangle ABCD.
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Diagonals are equal and also opposite sides are equal so it is a rectangle.
Show that A(–2, 3), B(8, 3) and C(6, 7) are the vertices of a right angled triangle.
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so it is a right angled triangle.
Find the value of m if the point (0, 2) is equidistant from (3, m) and (m, 5).
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If the point A (4, 3) and B(x, 5) are on the circle with centre O(2, 3), find the value of x.
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, centre
Three consecutive vertices of a parallelogram ABCD are A(1, 2), B(1, 0) and C(4, 0). Find the fourth vertex D.
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Mid point of
Also
Coordinates of
Which point on xaxis is equidistant from (7, 6) and (–3, 4)?
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Point
Find the ratio in which the line 2x + y = 4 divides the join of A(2, –2) and B(3, 7). Also, find the coordinates of the point of their intersection.
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Let the ratio be
Coordinates of the point of division
This point also lies on
coordinates
Find the value of k for which the distance between (9, 2) and (3, k) is 10 units.
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Find the ratio in which the point \(\left(\dfrac{2}{7},\dfrac{20}{7}\right) \) divides the join of (–2, –2) and (2, – 4).
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Find the coordinates of a point on xaxis which divides the line segment joining the points (–2, –3) and (1, 6) in the ratio 1 : 2.
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Coordinate of a point on xaxis
Coordinate of a point on xaxis
The line segment joining the points P(3, 3) and Q(6, – 6) is trisected at the points A and B such that A is nearer to P. If A also lies on the line given by 2x + y + k = 0, find the value of k.
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Since A lies on the line
Find the type of triangle formed by points A(–5, 6), B(– 4, –2), C(7, 5).
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All sides are different so it is a scales triangle.
In what ratio does the point (– 4, 6) divide the line segment joining the points A(– 6, 10) and B(3, –8)?
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