Solution:
The coordinates of the point P(x, y) which divides the line segment joining the points A(x₁, y₁ ) and B(x₂, y₂), internally, in the ratio m₁: m₂ is given by the Section Formula: P(x, y) = [(mx₂ + nx₁) / m + n, (my₂ + ny₁) / m + n]
Let the ratio be k : 1
Let the line segment be AB joining A (1, - 5) and B (- 4, 5)
By using the Section formula,
P (x, y) = [(mx₂ + nx₁) / m + n, (my₂ + ny₁) / m + n]
m = k, n = 1
Therefore, the coordinates of the point of division is
(x, 0) = [(- 4k + 1) / (k + 1), (5k - 5) / (k + 1)] ---------- (1)
We know that y-coordinate of any point on x-axis is 0.
Therefore, (5k - 5) / (k + 1) = 0
5k = 5
k = 1
Therefore, the x-axis divides the line segment in the ratio of 1 : 1.
To find the coordinates let's substitute the value of k in equation(1)
Required point = [(- 4(1) + 1) / (1 + 1), (5(1) - 5) / (1 + 1)]
= [(- 4 + 1) / 2, (5 - 5) / 2]
= [- 3/2, 0]
☛ Check: NCERT Solutions for Class 10 Maths Chapter 7
Video Solution:
Find the ratio in which the line segment joining A (1, - 5) and B (- 4, 5) is divided by the x-axis. Also find the coordinates of the point of division
NCERT Class 10 Maths Solutions Chapter 7 Exercise 7.2 Question 5
Summary:
The ratio in which the line segment joining A (1, - 5) and B (- 4, 5) is divided by the x-axis is 1:1 and the coordinates of the point of division is (-3/2, 0).
☛ Related Questions:
- If (1, 2), (4, y), (x, 6) and (3, 5) are the vertices of a parallelogram taken in order, find x and y.
- Find the coordinates of a point A, where AB is the diameter of a circle whose centre is (2, - 3) and B is (1, 4).
- If A and B are (- 2, - 2) and (2, - 4), respectively, find the coordinates of P such that AP = 3/7 AB and P lies on the line segment AB.
- Find the coordinates of the points which divide the line segment joining A (- 2, 2) and B (2, 8) into four equal parts.
In what ratio is the join of (4, 3) and (2, -6) divided by the x-axis. Also, find the co-ordinates of the point of intersection.
Let the point P (x, 0) on x-axis divides the line segment joining A (4, 3) and B (2, -6) in the ratio k: 1.
Using section formula, we have:
`0=(-6k+3)/(k+1)`
`0=-6k+3`
`k=1/2`
Thus, the required ratio is 1: 2.
Also, we have:
`x=(2k+4)/(k+1)`
`x=(2xx1/2+4)/(1/2+1)`
`x=10/3`
Thus, the required co-ordinates of the point of intersection are `(10/3,0)`
Is there an error in this question or solution?
Page 2
Find the ratio in which the join of (-4, 7) and (3, 0) is divided by the y-axis. Also, find the coordinates of the point of intersection.
`0=(3k-4)/(k+1)`
`3k=4`
`k=4/3` ..............(1)
`y=(0+7)/(k+1)`
`y=7/(4/3+1)` (from eq. 1)
`y=3`
Hence, the required is 4:3 and the required point is S(0, 3)
Is there an error in this question or solution?
Click here to get PDF DOWNLOAD for all questions and answers of this Book - ICSE Class 10 MATHS
Show More