Advertisements
Advertisements
Question
Find the ratio in which the x-axis divides internally the line joining points A (6, -4) and B ( -3, 8).
Solution
Let 'P'lies on x-axis
∴ Let P = (x, 0)
y = `("my"_2 + "ny"_1)/("m + n")`
`0 = (8"m" - 4"n")/("m + n")`
0 = 8m + 4n
∴ 4n = 8m
`4/8 = "m"/"n"`
`"m"/"n" = 1/2`
Ratio = m : n = 1 : 2
APPEARS IN
RELATED QUESTIONS
Determine the ratio in which the line 3x + y – 9 = 0 divides the segment joining the points (1, 3) and (2, 7)
Find the coordinates of the points which divide the line segment joining A (−2, 2) and B (2, 8) into four equal parts.
If two vertices of a parallelogram are (3, 2) (-1, 0) and the diagonals cut at (2, -5), find the other vertices of the parallelogram.
Show that the line segment joining the points (–5, 8) and (10, −4) is trisected by the co-ordinate axes.
A line segment joining A`(-1,5/3)` and B(a, 5) is divided in the ratio 1 : 3 at P, the point where the line segment AB intersects the y-axis.
- Calculate the value of ‘a’.
- Calculate the co-ordinates of ‘P’.
The mid-point of the segment AB, as shown in diagram, is C(4, –3). Write down the co-ordinates of A and B.
A (2, 5), B (-1, 2) and C (5, 8) are the vertices of triangle ABC. Point P and Q lie on AB and AC respectively, such that AP: PB = AQ: QC = 1: 2. Calculate the coordinates of P and Q. Also, show that 3PQ = BC.
A line intersects the y-axis and x-axis at the points P and Q respectively. If (2, -5) is the mid-point of PQ, then the coordinates of P and Q are respectively.
If the points A(1, 2), O(0, 0), C(a, b) are collinear, then ______.
The points A(x1, y1), B(x2, y2) and C(x3, y3) are the vertices of ∆ABC. What are the coordinates of the centroid of the triangle ABC?
