Q1:
Assertion (A): The ordinate of a point A on yaxis is 5 and B has coordinates (–3, 1). Then the length of AB is 5 units.
Reason (R): The point A(2, 7) lies on the perpendicular bisector of line segment joining the points P(6, 5) and Q(0, –4).
Q2:
Assertion : The area of the triangle with vertices (5 , 1), (3, 5), (5, 2), is 32 square units.Reason : The point (x, y) divides the line segment joining the points (x_{1}, y_{1}) and (x_{2}, y_{2}) in the ratio k : 1 externally then
Q3:
Assertion : The coordinates of the point which divides the join of A(5, 11) and B(4,7) in the ratio 7 : 2 is (2, 3) Reason : The coordinates of the point P(x, y) which divides the line segment joining the points A(x_{1}, y_{1}) and B(x_{2}, y_{2}) in the ratio m_{1} : m_{2} is
Q4:
Assertion (A): △ABC with vertices A(–2, 0), B(2, 0) and C(0, 2) is similar to △DEF with vertices D(–4, 0), E(4, 0) and F(0, 4).
Reason (R): 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.
Q5:
Assertion : The points (k, 2 2k), ( k+ 1,2k) and ( 4  k, 6  2k) are collinear if k = 1/2. Reason : Three points A,B and C are collinear in same straight line, if AB + BC = AC.
Q6:
Assertion : If the points A(4, 3) and B(x, 5) lies on a circle with the centre O(2,3) then the value of x is 2.
Reason : The midpoint of the line segment joining the points P(x_{1}, y_{1}) and Q(x_{2}, y_{2}) is
Q7:
Assertion (A): If the distance between the point (4, p) and (1, 0) is 5, then the value of p is 4.
Reason (R): The point which divides the line segment joining the points (7, – 6) and (3, 4) in ratio 1 : 2 internally lies in the fourth quadrant.
Q8:
Assertion : Centroid of a triangle formed by the points (a, b) (b, c), and (c, a) is at origin, Then a + b + c = 0 .
Reason : Centroid of a △ABC with vertices A (x_{1}, y_{1}), B(x_{2}, y_{2}) and C (x_{3}, y_{3}) is given by
Q9:
Assertion : The possible values of x for which the distance between the points A(x, 1) and B(5, 3) is 5 units are 2 and 8.
Reason : Distance between two given points A(x_{1}, y_{1}) and B(x_{2}, y_{2}) is given by,
Q10:
Assertion : Midpoint of a line segment divides line in the ratio 1 : 1.
Reason : If area of triangle is zero that means points are collinear.
Q11:
Assertion : The point (1, 6) divides the line segment joining the points (3, 10) and (6, 8) in the ratio 2 : 7 internally.
Reason : Three points A,B and C are collinear if AB + BC = AC
Q12:
Assertion : The point (1, 6) divides the line segment joining the points (3, 10) and (6, 8) in the ratio 2 :7 internally.
Reason : Three points A,B and C are collinear if area of △ ABC = 0 .
Q13:
Assertion : The value of y is 6, for which the distance between the points P(2, 3) and Q(10, y) is 10.
Reason : Distance between two given points A(x_{1}, y_{1}) and B(x_{2}, y_{2}) is given by,
Q14:
Assertion : If A (2a, 4a) and B (2a, 6a) are two vertices of a equilateral triangle ABC then the vertex C is given by (2a + a√3, 5a).
Reason : In equilateral triangle all the coordinates of three vertices can be rational.
Q15:
Assertion : The point (0, 4) lies on y axis.
Reason : The x coordinate on the point on y axis is zero.
Q16:
Assertion : The value of y is 6, for which the distance between the points P(2, 3) and Q(10, y) is 10.
Reason : Distance between two given points A (x_{1}, y_{1}) and B(x_{2}, y_{2}) is given 6,
Q17:
Assertion : C is the midpoint of PQ, if P is (4, x), C is (y, 1) and Q is ( 2, 4), then x and y respectively are 6 and 1.
Reason : The midpoint of the line segment joining the points P(x_{1}, y_{1}) and Q(x_{2}, y_{2}) is
Q18:
Assertion : The point (0, 4) lies on y axis.
Reason : The x coordinate on the point on y axis is zero.
Q19:
Assertion : Ratio in which the line 3x + 4y = 7 divides the line segment joining the points (1, 2) and ( 2, 1) is 3 : 5Reason : The coordinates of the point P(x, y) which divides the line segment joining the points A(x_{1}, y_{1}) and B(x_{2}, y_{2}) in the ratio m_{1} : m2_{ }is
Q20:
Assertion: The point which divides the line joining the points A(1, 2) and B( 1, 1) internally in the ratio 1: 2 is
Reason : The coordinates of the point P(x, y) which divides the line segment joining the points A(x_{1}, y_{1}) and B(x_{2}, y_{2}) in the ratio m_{1} : m_{2 }is
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