Find the distance between the following pairs of the point :
(i) (-3,6) and (2,-6)
(ii) (-a,-b) and (a,b)
(iii) ( ?/ ? ,2) and ( −?/ ? , 1( ?)/ (?) )
(iv) (√? + 1,1) and (0, √?)
Find the coordinates of the points on the y-axis, which are at a distance of 10 units from the point (-8, 4).
A point P (2, -1) is equidistant from the points (a, 7) and (-3, a). Find a.
Show that the points P (0, 5), Q (5, 10) and R (6, 3) are the vertices of an isosceles triangle
Prove that the points A (1, -3), B (-3, 0) and C (4, 1) are the vertices of an isosceles right-angled triangle. Find the area of the triangle.
The vertices of a triangle are (5, 1), (11, 1), and (11, 9). Find the coordinates of the circumcentre of the triangle.
The centre of a circle is (2x – 1, 3x + 1). Find x if the circle passes through (-3, -1) and the length of its diameter is 20 units.
The length of line PQ is 10 units and the co-ordinates of P are (2, -3); calculate the coordinates of point Q, if its abscissa is 10.
Point P (2, -7) is the center of a circle with a radius 13 unit, PT is perpendicular to chord AB and T = (-2, -4); calculate the length of:
(i) AT
(ii) AB
Calculate the distance between the points P (2, 2) and Q (5, 4) correct to three significant figures
Calculate the distance between A (7, 3) and B on the x-axis whose abscissa is 11.
Calculate the distance between A (5, -3) and B on the y-axis whose ordinate is 9.
Find the point on the y-axis whose distances from points A (6, 7) and B (4, -3) are in the ratio 1: 2.
The distances of point P (x, y) from the points A (1, -3) and B (-2, 2) are in the ratio 2: 3. Show that:
5×2 +5y2 -34x + 70y + 58 = 0.
The points A (3, 0), B (a, -2) and C (4, -1) are the vertices of triangle ABC right angled at vertex A. Find the value of a.
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