$CATEGORY: Maths - TicTacLearn/7. Coordinate geometry/7. Coordinate geometry--Section Formula

//Multiple Choice

The section formula divides a line segment in the ratio m\:n  such that the coordinates of the point dividing the segment joining A(x1,y1) and B(x2,y2) are\: {
= [ (mx1+nx2)/m+n,   (my1+ny2)/m+n ]
~ [ (nx1+mx2)/m+n,   (ny1+my2)/m+n ]
~ [(mx2-nx1)/m+n,   (my2-ny1)/m+n ]
~ None of the above
}

 The coordinates of the midpoint of a line segment joining (x1,y1) and (x2,y2) are\: {
~ (x1+x2, y1+y2)
= [(x1+x2)/2, (y1+y2)/2)]
~ [(x1−x2)/2, (y1−y2)/2)]
~ None of the above
}

 If P(x,y) divides the line segment joining A(2,3) and B(6,7) in the ratio 2\:3, the coordinates of P are\: 
{
~ (3,4)
= (4,5)
~ (5,6)
~ (6,7)
}

 If a point divides a line segment in the ratio 1\:1, the point is\: {
= Midpoint
~ Endpoint
~ Trisection point
~ None of these
}

 In a straight line, the section formula is valid only for points\: {
= On the line segment
~ Outside the line segment
~ On the x-axis
~ On the y-axis
}

 The ratio in which the point (5,−2) divides the line joining (2,−3) and (7,1) is\: {
~ 1\:1
~ 2\:3
= 3\:2
~ 4\:1
}

//True or False

The section formula is applicable only in two-dimensional geometry. {F}

The midpoint of a line segment is always equidistant from both endpoints. {T}

The external division of a line segment requires m≠nm\neq nm\=n. {F}

The section formula divides a line segment into equal parts regardless of the ratio. {F}

The section formula is valid for both internal and external division of a line segment. {T}

//Numericals



//Fill in the blanks

The section formula is used to find the coordinates of a point dividing a line segment in a given ______. {
     ~ Slope
     = Ratio
     ~ Direction
     ~ Midpoint
}

 A point dividing a line segment in the ratio 1\:1 is called the ______. {
     = Midpoint
     ~ Trisection point
     ~ Endpoint
     ~ Section point
}

 The coordinates of the midpoint of a line segment joining (x1,y1) and (x2,y2)  are given by  {
~ x₁ + x₂
~ y₁ + y₂
~ y₁ - y₂
= [ (x1+x2)/2, (y1+y2)/2) ]
}

 The section formula is derived using the concept of ______ ratios. {
     ~ Similar
     ~ Direct
     ~ Parallel
     = Proportional
}

//Match the following

Match the following items from Column A with their correct corresponding options from Column B\:
{
=Midpoint formula -> Ratio 1\:1
=Internal division -> Proportional division
=Geometry concept used -> Pythagoras theorem
}



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