QQuestion
In the given graph, P and Q are points such that PQ cuts off intercepts of 5 units and 3 units along the x-axis and y-axis respectively. Line RS is perpendicular to PQ and passes through the origin.
[Graph as given in the question paper]
Find:
(a) the coordinates of P and Q.
(b) the equation of RS.
✓Answer
(a) From the graph:
P = (5, 0) and Q = (0, −3).
(b) Slope of PQ = \frac{-3-0}{0-5}=\frac{-3}{-5}=\frac{3}{5}
Since RS is perpendicular to PQ:
Slope of RS × \frac{3}{5} = −1
⇒ Slope of RS = -\frac{5}{3}
RS passes through the origin (0, 0).
Using y − y₁ = m(x − x₁):
y − 0 = -\frac{5}{3}(x − 0)
⇒ y = -\frac{5\mathrm{x}}{3}
⇒ 3y = −5x
⇒ 5x + 3y = 0
Therefore, the equation of RS is 5x + 3y = 0.
Related Questions
More ICSE Moderate level questions
(a) If the lines kx − y + 4 = 0 and 2y = 6x + 7 are perpendicular to each other, find the value of k. (b) Find the equation of a line parallel to 2y = 6x + 7 and passing through (−1, 1).
The points A(x, y), B(3, −2) and C(4, −5) are collinear. Then y in terms of x is: (a) 3x − 11 (b) 11 − 3x (c) 3x − 7 (d) 7 − 3x
The equation of the line passing through the origin and parallel to the line 3x + 4y + 7 = 0 is: (a) 3x + 4y + 5 = 0 (b) 4x − 3y − 5 = 0 (c) 4x − 3y = 0 (d) 3x + 4y = 0
In the given graph, ABCD is a parallelogram.[Graph as given in the question paper](a) Write the coordinates of A, B, C and D.(b) Calculate the coordinates of P, the intersection of diagonals AC and BD.(c) Find the slopes of CB and DA and verify that they are parallel.(d) Find the equation of diagonal AC.
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.
For the following frequency distribution, find:(a) the mean, to the nearest whole number.(b) the median.x10111213141516f3226353
Solve the quadratic equation 2x² − 5x − 4 = 0. Give your answers correct to three significant figures.
A man bought ₹200 shares of a company at 25% premium. He received a return of 5% on his investment. Find:(a) the market value of one share.(b) the dividend percentage declared.(c) the number of shares purchased if the annual dividend is ₹1,000.
The first term of an Arithmetic Progression is 5, the last term is 50 and the sum is 440. Find:(a) the number of terms.(b) the common difference.
Assertion (A): If sin² A + sin A = 1, then cos⁴ A + cos² A = 1. Reason (R): 1 − sin² A = cos² A. (a) A is true, R is false. (b) A is false, R is true. (c) Both A and R are true, and R is the correct reason for A. (d) Both A and R are true, and R is not the correct reason for A.
A man invested in a company paying 12% dividend on its shares. If the percentage return on his investment is 10%, then the shares are: (a) at par (b) below par (c) above par (d) cannot be determined