Section Formula

The coordinates of the point which divides the line segment joining the points A (6, 3) and B (─ 4, 5) internally in the ratio 3 : 2 are :

• $\left(\frac{21}{5},\ 0\right)$

• $\left(0,\frac{21}{5}\right)$

• $\left(2,\frac{19}{5}\right)$

• $\left(\frac{24}{5},\frac{21}{5}\right)$

If the mid-point of the line segment joining the points (3a, 4) and (─ 1, 2b) is (1, 2a + 3), then the values of a and b are :

• $\frac{1}{3}\ and\ -\frac{5}{3}$

• $0\ and\ -\frac{7}{2}$

• $1\ and\ 3$

• $\frac{2}{3}\ and\ \frac{1}{6}$

The coordinates of the point of intersection of the y-axis with the line segment joining the points (─ 4, 5) and

(3, ─ 7) are :

• $\left(0,\ -\frac{13}{7}\right)$

• $\left(-\frac{13}{12},\ 0\right)$

• $\left(-\frac{13}{7},\ 0\right)$

• $\left(0,\ -\frac{1}{7}\right)$

In what ratio does the x-axis divide the line segment joining the points (─ 4, 3) and ( 8, ─ 6) ?

• $2\ :\ 1$

• $1\ :\ 2$

• $3\ :\ 1$

• $1\ :\ 3$

If the three consecutive vertices of a parallelogram ABCD are A (─ 1, 0), B (3, 1) and C (2, 2), then the coordinates of the fourth vertex D are :

• $\left(2,\ 1\right)$

• $\left(0,\ -1\right)$

• $\left(4,\ 3\right)$

• $\left(-2,\ 1\right)$

If the coordinates of one end of a diameter of a circle are

(4, ─ 1) and the coordinates of the centre of the circle are (1, ─ 3), then the coordinates of the other end of the diameter are :

• $\left(2,\ -7\right)$

• $\left(-2,\ -5\right)$

• $\left(\frac{5}{2},\ -2\right)$

• $\left(5,\ -4\right)$

If the three vertices of a triangle are (5, ─ 1), (─ 3, ─ 2) and (─ 1, 8), then the coordinates of its centroid are :

• $\left(3,\ \frac{11}{3}\right)$

• $\left(\frac{1}{3},\ \frac{5}{3}\right)$

• $\left(1,\ 5\right)$

• $\left(3,\ -\frac{7}{3}\right)$

The ratio in which the point  $\left(-3,\ \frac{2}{3}\right)$ divides the line segment joining the points (─ 5, ─ 4) and  (─ 2, 3)  internally is :

•  $2\ :\ 3$  

•  $1\ :\ 2$  

• 2 : 1

• 3 : 1

The coordinates of the points of trisection of the line segment joining the points (1, ─ 2) and (─ 3, 4) are :

• $\left(-\frac{1}{3},0\right)\ and\ \left(-\frac{5}{3},\ 2\right)$

• $\left(-1,\ 1\right)\ and\ \left(-2,\ 3\right)$

• $\left(\frac{4}{3},\ 2\right)\ and\ \left(2,\ 3\right)$

• $\left(2,\ -3\right)\ and\ \left(\frac{5}{2},\ -\frac{7}{2}\right)$

: If x ─ 5y + k = 0 is a median of the triangle whose vertices are (2, 5), (─ 4, 9) and (─ 2, ─ 1), then the value of ‘k’ is :

• $-23$

• 23

• 49

• 61