Coordinate geometry is ........ tool for studying geometry.

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an algebraical

In the fourth quadrant for a point, the abscissa is ....... and the ordinate is ........

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positive, negative

If the point (0, 0), (1, 2) and (x, y) are collinear, then find x.

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\(\therefore \quad \frac { 1 }{ 2 } \left[ { { x }_{ 1 }\left( { y }_{ 2 }-{ y }_{ 3 } \right) +{ x }_{ 2 }\left( { y }_{ 3 }-{ y }_{ 1 } \right) +{ x }_{ 3 }\left( { y }_{ 1 }-{ y }_{ 2 } \right) } \right] =0\)
\(\Rightarrow \quad \frac{1}{2}[0(2-y)+1(y-0)+x(0-2)]=0\)
\(\Rightarrow \quad \frac { 1 }{ 2 }[y-2x]=0\)
\(\Rightarrow \quad 2x-y=0\)
 

A circle has its centre at the origin and a point P(5,0) lies on it. The point Q(6,8) lies outside the circle. State whether true or false. Justify your answer.

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True because distance between centre (origin) and Q(6,8) is greater than its radius. i.e., 5

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.

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Find the distance between (-5, 0) and (5, 0).

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5 units

Point (m, 2) lies on the line 3x - 8y = 2, find the value of m.

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m = 6

If origin is the mid-point of the line segment joined by  the points (2, 3) and (x, y), then find the values of x and y.

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(-2, -3)

Find the distance between the points (0, 5) and (-5, 0).

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\(5\sqrt { 2 }\ \ units\)

Find the perimeter of the triangle with vertices (0,6), (0,0) and (8,0)

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If the vertices of a triangle are (8,7), (8,-2) and (2,-2), then find the coordinates of its centroid.

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Find the value of x for which the distance between the points P(2,-3) and Q(x,5) is 10 units.

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Find the perpendicular distance of A(5, 12) from the Y-axis.

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Find the centroid of a triangle whose vertices are (3, -7), (-8, 6) and (5, 10).

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What is the distance between the points \((10\ { 30° } ,0)\) and \((0,\ 10\ \cos{ 60° } )\) ?

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Find the distance between the following pairs of points: (2,3),(4,1)

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Show that the points A(2,-2), B(14,10), C(11,13) abd D(-1,1) are the vertices of a rectangle

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Find the coordinates of the points of trisection of the line segment joining (4,-1) and (-2,-3)

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If the point C(-1,2) divides the line segment AB in the ratio 3:4, where the coordinates of A are (2,5), find the coordinates of B.

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Find the value of p for which the point (-1,3), (2,p) and (5,-1) are collinear.

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If two vertices of an equilateral triangle are (0,0), \((3,\sqrt3)\) find the area of the triangle.

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Determine, whether the triangle whose vertices are given is isosceles: (10, -18), (3, 6) and (-5, 2).

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Points P,Q,R and S divide the line segment joining the points A(1,2) and B(6,7) in 5 equal parts. Find the coordinates of the points P,Q and R.

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Find the value of 's' if the points P(1,0) is equidistant from Q(3,s) and R(s,-3).

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Find the coordinate of a point in x-axis which divides line segment joining the points (-2,-3) and (1,6) in ration 1 : 2. 

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Prove that (2,-2),(-2,1) and (5,2) are vertices of a right-angled triangle. Find the area of the triangle and the length of the hypotenuse.

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The base BC of an equilateral triangle ABC lies on y-axis. The coordinates of point C are (0,-3). The origin is the mid-point of the base. Find the coordinates of the points A and B. Also find the coordinates of another point D such that BACD is a rhombus.

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