QQuestion
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.
✓Answer
(a) D is the midpoint of B(0, 4) and C(−6, 4).
Using the midpoint formula:
D = \left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)
D = \left(\frac{0+(-6)}{2},\frac{4+4}{2}\right)
D = \left(\frac{-6}{2},\frac{8}{2}\right)
Therefore, D = (−3, 4).
(b) The median AD passes through A(1, −1) and D(−3, 4).
⇒ y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)
⇒ y-(-1)=\frac{4-(-1)}{-3-1}(x-1)
⇒ y+1=\frac{5}{-4}(x-1)
⇒ −4(y + 1) = 5(x − 1)
⇒ −4y − 4 = 5x − 5
⇒ 5x + 4y = 1
Therefore, the equation of median AD is 5x + 4y = 1.
Related Questions
More ICSE Easy level questions
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.
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
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)
(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).
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.
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
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.
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.
What number must be added to each of the numbers 4, 6, 8 and 11 so that the resulting four numbers are in proportion?
A bag contains 25 cards numbered from 1 to 25. A card is drawn at random. Find the probability that the number on the card drawn is: (a) a multiple of 5 (b) a perfect square (c) a prime number.
The following distribution gives the daily wages of 60 workers of a factory: Daily income (₹) Number of workers 200–300 6 300–400 10 400–500 14 500–600 16 600–700 10 700–800 4 Use graph paper. Take 2 cm = ₹100 along one axis and 2 cm = 2 workers along the other axis. Draw a histogram and hence find the mode of the distribution.
Using componendo and dividendo, solve for x: = 3