QQuestion
A(−10, −2) and B(2, 10) are two end points of a line segment. If AB intersects the x-axis at P, find the:
(a) ratio in which P divides AB.
(b) coordinates of point P.
ICSEClass XMathematicsSection Formula03 Mark2026 Moderate
✓Answer
(a) Let P(x, 0) divide AB internally in the ratio m : n.
Using the section formula for the y-coordinate,
y = \frac{\mathrm{m}\mathrm{y}_2+\mathrm{n}\mathrm{y}_1}{\mathrm{m}+\mathrm{n}}
Since P lies on the x-axis, y = 0.
0 = \frac{\mathrm{m}(10)+\mathrm{n}(-2)}{\mathrm{m}+\mathrm{n}}
⇒ 10m − 2n = 0
⇒ 10m = 2n
⇒ \frac{\mathrm{m}}{\mathrm{n}}=\frac{2}{10}=\frac{1}{5}
Therefore, P divides AB in the ratio 1 : 5.
(b) Using the section formula for the x-coordinate,
x = \frac{\mathrm{m}\mathrm{x}_2+\mathrm{n}\mathrm{x}_1}{\mathrm{m}+\mathrm{n}}
Here, m = 1, n = 5, x₁ = −10 and x₂ = 2.
x = \frac{1(2)+5(-10)}{1+5}
x = \frac{2-50}{6}
x = \frac{-48}{6} = −8
Since P lies on the x-axis, y = 0.
Therefore, P = (−8, 0).
Was this answer helpful?
Related Questions
More ICSE Moderate level questions
1/12
In the given figure, AOB is a right-angled triangle and C is the midpoint of the hypotenuse AB. If the coordinates of C are (x, y), the point equidistant from A, O and B is: (a) (x, y) (b) (y, x) (c) (x/2, y/2) (d) (2x/3, 2y/3)
The coordinates of the vertices of triangle ABC are respectively (−4, −2), (6, 2) and (4, 6). The centroid G of triangle ABC is: (a) (2, 2) (b) (2, 3) (c) (3, 3) (d) (0, −1)
ABC is a triangle whose vertices are A(1, −1), B(0, 4) and C(−6, 4). D is the midpoint of BC. Find: (a) the coordinates of D (b) the equation of the median AD.
A and B are two points on the x-axis and y-axis respectively, as shown in the figure. (a) Write down the coordinates of A and B. (b) P is a point on AB such that AP : PB = 3 : 1. Using the section formula, find the coordinates of P. (c) Find the equation of a line passing through P and perpendicular to AB.
In the given diagram, ABC is a triangle, where B(4, −4) and C(−4, −2). D is a point on AC. (a) Write down the coordinates of A and D. (b) Find the coordinates of the centroid of △ABC. (c) If D divides AC in the ratio k : 1, find the value of k. (d) Find the equation of the line BD.
The cost price of a TV set is ₹ 20,000. The shopkeeper marked it for ₹ 24,000. He sells it to a customer at a discount of 10% on the marked price. If the sale is intra-state and the rate of GST is 12%, find the: (a) discounted price of the TV set. (b) amount paid by the customer to clear the bill.
The histogram drawn on the graph represents the number of students of different heights (in cm). Using the graph, answer the following: (a) the number of students whose height is 150 cm and above. (b) the modal height. (c) the total number of students.
Use graph sheet for this question. Take 2 cm = 1 unit along both x and y axis. Graphically represent parallelogram OABC, where O(0, 0), A(2, 3), B(5, 3) and C(3, 0). Reflect OABC : (a) on the x-axis and name its image as ODEC. (b) through the origin and name its image as OIJH. (c) on the y-axis and name its image as OFGH.
The 4th and the 7th terms of an A.P. are 60 and 114 respectively. Find: (a) the first term and the common difference. (b) the sum of the first 10 terms.
The total surface area of a sphere S₁ of radius R and the total surface area of a solid hemisphere S₂ of radius r are equal. The ratio R : r is: (a) 1 : 1 (b) 2 : 1 (c) √3 : 2 (d) 2 : √3
Find the equation of a line whose y-intercept is 6 and is parallel to x-axis. (a) y = 6 (b) x = 6 (c) x + y = 6 (d) y − x = 6
Prove that: (sec θ − cos θ)(cosec θ − sin θ) = sin θ cos θ