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| Summary |
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- In coordinate geometry, the tools of algebra are used in studying geometry by establishing 1-1 correspondence between the points in a plane and the ordered pairs of real numbers.
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- If P(x1,y1) and Q(x2,y2) be any two points in the plane, then
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- If A(x1,y1), B(x2,y2) and C(x3,y3) be the vertices of a triangle, then area,
D, of triangle ABC is given by
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- The points A, B and C are collinear if and only if area of triangle ABC is zero.
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- A point R is said to divide PQ internally in the ratio m:n if R is within
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- If R(x,y) divides the join of P(x1,y1) and Q(x2,y2) internally in the
ratio m:n, then
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A point R is said to divide PQ externally
in the ratio m:n, where m ¹
n, if R is outside PQ and  |
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- If R(x,y) divides the join of P(x1,y1) and Q(x2,y2) externally in the
ratio m:n, where m ¹
n, then
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- If M(x,y) is the midpoint of the join of P(x1,y1) and Q(x2,y2), then
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- If A(x1,y1), B(x2,y2) and C(x3,y3) are the vertices of a triangle, then
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- Centroid =
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- Incentre
=
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| where a = BC, b = CA, c = AB |
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- When a point moves so as to always satisfy a given condition or conditions, the path it traces out is called its locus under these conditions.
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- If P(x,y) be any sample point on the locus, then an equation involving x and y which is satisfied by each point on the locus and such that each point satisfying the equation is on the locus is called the equation of the locus.
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- The slope of a non-vertical line is defined as the tangent of the angle which the line makes with the positive direction of the x-axis.
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- If a non-vertical line passes through two distinct points (x1,y1) and
(x1, y1), then the slope, m, of the line is given by
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- The slope of a horizontal line is zero.
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- The slope of a line making equal intercepts on the axes is '-1'.
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- The slope of a line equally inclined to the axes is either '1' or '-1'.
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- The slope of the line ax + by + c = 0, b
¹ 0 is equal to
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- Two non-vertical lines are parallel if and only if their slopes are equal.
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- Two non-vertical lines are perpendicular if and only if the product of their slopes is '-1'.
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