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

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(a)

an algebraical

The centroid of triangle divides the median in the ratio ...........

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(a)

2:1

.............. is the point of intersection of the axes of coordinates.

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origin

Area of triangle formed by the vertices (x1,y1), (x2,y2) and (x3,y3) is the numerical value of ................

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\({1\over2}[x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)]\)

The abscissa and ordinate of a point taken together is known as ............... of a point.

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coordinates

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

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positive, negative

Find the relation between x and y such that the point (x,y) is equidistant from the points (7,1) and (3,5).

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(a)

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

If A and B are the points(-6,7) and (-1,-5) respectively then find the distance 2AB.

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A(-6,7),B(-1,-5)
Let x₁=-6,y₁=7;x₂=-1,y₂=-5
Distance, \(AB=\sqrt { \left( { x }_{ 2 }-{ x }_{ 1 } \right) ^{ 2 }+\left( { y }_{ 2 }-{ y }_{ 1 } \right) ^{ 2 } } \)
\(=\sqrt { { 5 }^{ 2 }+\left( -12 \right) ^{ 2 } } =\sqrt { 25+144 } =\sqrt { 169 } =13\)
2AB=2x13=26

If the mid-point of the line segment joining the points P(6,b-2) and Q(-2,4) is (2,-3) find the value of b.

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