List of top Mathematics Questions on Section Formula

In the given figure, point D divides the side BC of $\Delta ABC$ in the ratio $1 : 2$. Find length AD.

The line segment joining the points $P(-4, -2)$ and $Q(10, 4)$ is divided by y-axis in the ratio

The line segment joining the points $P(-4, -2)$ and $Q(10, 4)$ is divided by y-axis in the ratio

The line segment joining the points $P(-4, -2)$ and $Q(10, 4)$ is divided by y-axis in the ratio

Find the ratio in which the x-axis divides the line segment joining the points ($-$6, 5) and ($-$4, $-$1). Also, find the point of intersection.

Let \[ \overrightarrow{OA}=\hat{i}+2\hat{j}-4\hat{k} \] and \[ \overrightarrow{OB}=3\hat{i}-4\hat{j}-2\hat{k} \] be the position vectors of points \(A\) and \(B\). If a point \(C\) divides the line segment \(AB\) in the ratio \(1:3\) externally, then the position vector of a point which divides \(OC\) in the ratio \(4:1\) internally is

Determine the ratio in which the line 3x + y - 9 = 0 divides the line segment joining the points (1, 3) and (2, 5). Find the point of intersection.

A point P divides the line segment joining the points A(-3, 5) and B(7, -4) in a certain ratio. If the point P lies on the line y = 2x, then find the ratio AP : PB and coordinates of point P.

A point P(x, 7) divides a line segment joining the points A(-5, 4) and B(7, 9) in a certain ratio. Find the ratio and hence find the value of x.

Find the coordinates of the points of trisection of the line segment joining the points A\(-1, 4\) and B\(-3, -2\).

Find the coordinates of the points of trisection of the line segment joining the points A\(-1, 4\) and B\(-3, -2\).

Parthi and Alisha found a treasure that is exactly on the straight line joining their locations. Parthi's location is at point $(-6, -5)$ and Alisha's location is at point $(10, 11)$. The distance from the treasure to Parthi's location is three times that of the distance to Alisha's location. Find the coordinates of the location of the treasure.

Find the ratio in which the $x$-axis divides the line segment joining the points $(-6, 5)$ and $(-4, -1)$. Also, find the point of intersection.

The ratio in which the x-axis divides the line segment joining the points A\(-8, 4\) and B\(-6, -2\) is :

The position vectors of the points $A$ and $B$ are $\vec{a} = 2\hat{i} - \lambda \hat{j} + 5\hat{k}$ and $\vec{b} = \mu \hat{i} + 7\hat{j} + 3\hat{k}$ respectively. If the position vector of the mid-point of the line segment $AB$ is $\vec{c} = 3\hat{i} + 2\hat{j} + 4\hat{k}$, then the value of $\lambda + \mu$ is equal to

Determine the ratio in which the line \(2x + y = 6\) divides the line segment joining the points (1, 3) and (2, 5).

Points \(P(6, 0)\), \(Q(2, 8)\) and \(R(-2, 4)\) are vertices of \(\Delta PQR\). It is given that \(MN \parallel QR\) such that \(\frac{PM}{MQ} = \frac{1}{3}\). Using distance formula and ratio formula, show that \(\frac{MN}{QR} = \frac{1}{4}\).

Points P(6, 0), Q(2, 8) and R(\(-2\), 4) are vertices of \(\triangle\)PQR. It is given that MN $\parallel$ QR such that \(\frac{PM}{MQ} = \frac{1}{3}\). Using distance formula and ratio formula, show that \(\frac{MN}{QR} = \frac{1}{4}\).

If the position vectors of the points P and Q are, respectively, \(5\vec{a} - 6\vec{b}\) and \(\vec{a} + 2\vec{b}\), then the point R with position vector \(2\vec{a}\) divides the line segment joining P and Q internally in the ratio

The ratio in which the point \[ (3,4) \] divides the line segment joining \[ (1,2) \] and \[ (5,6) \] is:

The coordinates of the points of trisection of the line segment joining the points $ (3, 2) $ and $ (6, -4) $ are

Let $O$ be the origin. Let $\overrightarrow{OA} = \vec{a}$ and $\overrightarrow{OB} = \vec{b}$ be the position vectors of the points $A$ and $B$ respectively. A point $P$ divides the line segment $AB$ internally in the ratio $m:n$. Then $\overrightarrow{AP}$ is equal to:

If \(A, B, C\) are vertices of a triangle with position vectors \(\vec a, \vec b, \vec c\), find the position vector of the point \(D\) where the angle bisector from vertex \(A\) meets \(BC\).

Let $P(1,2)$, $Q(a,b)$, $R(5,7)$ and $S(2,3)$ be the vertices of a parallelogram $PQRS$. Then ________.

P divides AC in 3:4 and Q divides BC in 4:3. Then M divides AQ in the ratio