21)

 

The length of the median through A of \(\triangle\)ABC with vertices A(7, -3), B(5, 3) and C(3, -1) is

Class 10 Maths

A)

5 units

B)

15 units

C)

25 units

D)

35 units

22)

 

The centroid of a triangle whose vertices are (x1, y1), (x2, y2) and (x3, y3) is given by

Class 10 Maths

A)

\(\left( {\frac{{{x_1} + {x_2} + {x_3}}}{3},\frac{{{y_1} + {y_2} + {y_3}}}{5}} \right)\)

B)

\(\left( {\frac{{{x_1} + {x_2} + {x_3}}}{3},\frac{{{y_1} + {y_2} + {y_3}}}{3}} \right)\)

C)

\(\left( {\frac{{{x_1} + {x_2} + {x_3}}}{5},\frac{{{y_1} + {y_2} + {y_3}}}{3}} \right)\)

D)

\(\left( {\frac{{{x_1} + {x_2} + {x_3}}}{5},\frac{{{y_1} + {y_2} + {y_3}}}{4}} \right)\)

23)

 

If x is a positive integer such that the distance between points P (x, 2) and Q (3, - 6) is 10 units, then x =

Class 10 Maths

A)

-19

B)

-9

C)

9

D)

19

E)

none of the above

24)

Three consecutive vertices of a parallelogram ABCD are A(1, 2), B(1, 0) and C(4, 0). The co – ordinates of the fourth vertex D are

Class 10 Maths

A)

(4, 2)

B)

(-4, -2)

C)

(4, -2)

D)

(-4, 2)

25)

If the point R(x, y) divides the join of P(x1, y1) and Q(x2, y2) internally in the given ratio m1 : m2, then the coordinates of the point R are

Class 10 Maths

A)

\(\left( {\frac{{{m_2}{x_1} - {m_1}{x_2}}}{{{m_1} - {m_2}}},\frac{{{m_2}{y_1} - {m_1}{y_2}}}{{{m_1} - {m_2}}}} \right)\)

B)

\(\left( {\frac{{{m_2}{x_1} + {m_1}{x_2}}}{{{m_1} + {m_2}}},\frac{{{m_2}{y_1} + {m_1}{y_2}}}{{{m_1} + {m_2}}}} \right)\)

C)

\(\left( {\frac{{{m_2}{x_1} - {m_1}{x_2}}}{{{m_1} + {m_2}}},\frac{{{m_2}{y_1} - {m_1}{y_2}}}{{{m_1} + {m_2}}}} \right)\)

D)

None of these

26)

The fourth vertex D of a parallelogram ABCD whose three vertices are A (-2, 3), B (6, 7) and C (8, 3) is

Class 10 Maths

A)

(0, 1)

B)

(0, -1)

C)

(1, -1)

D)

(-2, -1)

27)

If the points (k, 2k), (3k, 3k) and (3, 1) are collinear, then k

Class 10 Maths

A)

\(\frac{-3}{3}\)

B)

\(\frac{-1}{5}\)

C)

\(\frac{-1}{3}\)

D)

\(\frac{-11}{3}\)

28)

The coordinates of the mid-point of the line segment joining the points (x1, y1) and (x2, y2) is given by

Class 10 Maths

A)

\(\left( {\frac{{{x_1} + {x_2}}}{2},\frac{{{y_1} + {y_2}}}{2}} \right)\)

B)

\(\left( {\frac{{{x_1} + {x_2}}}{2},\frac{{{y_1} + {y_2}}}{5}} \right)\)

C)

\(\left( {\frac{{{x_1} + {x_2}}}{12},\frac{{{y_1} + {y_2}}}{2}} \right)\)

D)

\(\left( {\frac{{{x_1} + {x_2}}}{5},\frac{{{y_1} + {y_2}}}{5}} \right)\)

29)

The point on the x-axis which is equidistant from points (-1, 0) and (5, 0) is

Class 10 Maths

A)

(2, 8)

B)

(2, 5)

C)

(-2, 0)

D)

(2, 0)

30)

If the points A(2, 3), B(5, k) and C (6,7) are the collinear then

Class 10 Maths

A)

k = 64

B)

k = 6

C)

k = 46

D)

k = 5