Finding Ratio Given the Points

Q. The ratio in which the line segment joining A(-3 , 10) and B (6 , -8) is divided by P (-1 , 6) is .

1. 2 : 7
2. 3 : 5
3. 2 : 3

Q. Question 4
Find the ratio in which the line segment joining points (-3, 10) and (6, - 8) is divided by (-1, 6).

Q.

The midpoint of the line joining the points $(-10,8)$ and $(-6,12)$ divides the line joining the points $(4,-2)$ and $(-2,4)$ in the ratio

1. $1:2$ internally

2. $1:2$ externally

3. $2:1$ internally

4. $2:1$ externally

5. $2:3$ externally

Q.

Question 8
If A and B are (–2, –2) and (2, –4) respectively, find the coordinates of P such that $AP=\frac{3}{7}AB$ and P lies on the line segment AB.

Q.

Let P be a plane $lx+my+nz=0$ containing the line, $\frac{\left[1-x\right]}{1}=\frac{\left[y+4\right]}{2}=\frac{\left[z+2\right]}{3}$. If plane $P$ divides the line segment $AB$ joining points $A\left(-3,-6,1\right)$ and $B\left(2,4,-3\right)$ in ratio $k:1$ then the value of $k$ is equal to :

1. $1.5$

2. $2$

3. $4$

4. $3$

Q.

Determine the ratio in which the point P (m, 6) divides the join A (-4, 3) and B (2, 8), also find the value of m.

Q.

In $△ABC,G$ is the centroid, $D$ is the midpoint of $BC$. If $A=\left(2,3\right)$ and $G=\left(7,5\right)$, then the point $D$ is

1. $\left(\frac{9}{2},4\right)$

2. $\left(\frac{19}{2},6\right)$

3. $\left(\frac{11}{2},\frac{11}{2}\right)$

4. $\left(8,\frac{13}{2}\right)$

Q. Determine the ratio in which the point (−6, a) divides the join of A (−3, 1) and B (−8, 9). Also find the value of a.

Q.

find the ratio in which the point P(3/4, 5/12) divides the line segment joining the points A(1/2, 3/2) and B(2, -5)

Q. Find the ratio in which the point P(1, 2) divides the line joining the points A(-2, 1) and B(7, 4).

1. 1:2
2. 2:3
3. 3:4
4. 1:3

Q. If P (x, 6) is the mid-point of the line segment joining A (6, 5) and B (4, y), find y.

Q.

If $(x,y)$ are any point on the parabola $y^2=4x$. Let $P$ be the point that divides the line segment from $(0,0)\mathrm{to}(x,y)$ in the ratio $1:3$. Then, the locus of $P$ is:

1. $x^2=y$

2. $y^2=2xy$

3. $y^2=x$

4. $x^2=2y$

Q. determine the ratio in which the point P(m, 6) divides the join of A(-4, 3) and B(2, 8).also, find the value of m.

Q. The ratio in which the line segment joining A(-3 , 10) and B (6 , -8) is divided by P (-1 , 6) is .

1. 2 : 7
2. 3 : 5
3. 2 : 3

Q. The ratio in which the point (8, 7) divides the line segment joining the points $(\frac{28}{3},\frac{22}{3})and(\frac{20}{3},\frac{20}{3})$ is k:1. The value of k is _

Q.

In what ratio does the point (a, 6) divide the join of (-4, 3) and (2, 8) ? Also, find the value of a.

Q.

In what ratio the line segment joining the points (-1, 3) and (4, -7) divided by the point (2, -3)?

1. 2:7

2. 3:5

3. 5:3

4. 3:2

Q. Find the coordinates of the point that divides the line segment joining the points (𝟒, −𝟑) and (𝟖, 𝟓) in the ratio 𝟑:𝟏 internally.

Q.

The line segment joining the points M (5, 7) and N (-3, 2) is intersected by the y-axis at point L. Write down the abscissa of L. Hence, find the ratio in which L divides MN. Also, find the co-ordinates of L.

Q. Given a line segment AB joining the points A(-4, 6) and B(8, -3). Find:
(i) the ratio in which AB is divided by the y-axis
(ii) the coordinates of the point of intersection
(iii) the length of AB
[4 MARKS]

Q.

The ratio in which the line segment joining the points (1, – 7) and (6, 4) is divided by x-axis is _____.

1. 3:1

2. 2:3

3. 7:2

4. 7:4

Q.

In an examination hall, students are seated at a distance of 2 m from each other, to maintain the social distance due to CORONA virus pandemic. Let three students sit at points A, B and C whose coordinates are (4, -3), (7, 3), and (8, 5) respectively.

Based on the above information, answer the following questions.
(Q) If an invigilator at the point I, lying on the straight line joining B and C such that it divides the distance between them in the ratio of 1 : 2. Then coordinates of I are:

1. $(\frac{22}{3},\frac{11}{3})$
2. $(6,1)$
3. $(\frac{22}{3},\frac{13}{3})$
4. $(9,1)$

Q. Find the equation of a line which divides the line segment joining the points (1, 1) and (2, 3) in the ratio 2:3 perpendicularly.

Q. Question 11
Find the ratio in which the point $P(\frac{3}{4},\frac{5}{12})$
divides the line segment joining the points $A(\frac{1}{2},\frac{3}{2})$ and B(2, -5).

Q. In what ratio does the point P(p, -1) divides the line segment joining the points A(1, -3) B(6, 2) hence find value of p?

Q. The line segment joining $(2,-3)$ and $(5,6)$ is divided by x-axis in the ratio:

1. $2:1$
2. $1:2$
3. $3:1$
4. $1:3$

Q. 3.Find the ratio in which (7/3, -1) divides the line joining the points (1, 5) and (3, -4)

Q.

The ratio in which the line segment joining the points (1, – 7) and (6, 4) is divided by the x-axis is ___.

1. 7:2

2. 3:1

3. 7:4

4. 2:3

Q.

Determine the ratio in which the graph of the equation $3x+y=9$ divides the line segment joining the points $A(2,7)$ and $B(1,3)$.

1. $\frac{4}{3}$
2. $\frac{2}{3}$
3. $\frac{1}{3}$
4. $\frac{3}{4}$

Q. Find the ratio in which the line 2x+3y-5 = 0 divides the line segment joining the points A(8, -9) and B(2, 1).
If the ratio is m:n, then, m = ___.

1. 1
2. 2
3. 8
4. 6