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

//Multiple Choice

The distance of the point (3,4) from the origin is\: {
     ~ 3
     ~ 4
     = 5
     ~ 7
}

 If two points are (1,2) and (1,−3), their distance is\: {
     = 5
     ~ 4
     ~ 3
     ~ 6
}

 In a coordinate plane, the distance between A(−2,1) and B(2,1) is\: {
     ~ 2
     = 4
     ~ 5
     ~ 6
}

 The distance formula can be derived using which geometric principle? {
     = Pythagoras theorem
     ~ Similar triangles
     ~ Trigonometry
     ~ Arithmetic progression
}

If the distance between A(2,−1)and B(x,3) is 5, the value of x is\: {
    ~ 6 or -2
    = 4 or -2
    ~ 5 or -3
    ~ 3 or -3
}

//True or False

The distance formula is derived from the Pythagoras theorem. {T}

The distance between two points can be negative. {F}

The distance between A(x,y) and the origin is x2+y2 . {F}

The distance between two points on the same vertical line is equal to the absolute difference of their y-coordinates. {T}

If the distance between two points is zero, the points are coincident. {T}

//Numericals



//Fill in the blanks

The distance between two points on the x-axis, (x1,0) and (x2,0), is  ______. {
     ~ x₁
     ~ y₁
     ~ y₂
     = x₂-x₁
}

 If the coordinates of two points are (0,5) and (0,−5), their distance is ______. {
     ~ 5
     ~ 0
     = 10
     ~ 25
}

 The distance between two points in a plane is always ______. {
     ~ Negative
     = Non-negative
     ~ Zero
     ~ Undefined
}

//Match the following

Match the following items from Column A with their correct corresponding options from Column B\:
{
=Distance formula -> squareroot((x2−x1)^2 + (y2−y1)^2)
=Origin -> (0,0)
=Points on x-axis -> Same y-coordinates
=Points on y-axis -> Same x-coordinates
=Pythagoras theorem -> Basis of distance formula
}



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