Advertisements
Advertisements
Question
If A = (−4, 3) and B = (8, −6)
- Find the length of AB.
- In what ratio is the line joining A and B, divided by the x-axis?
Solution
i. A (−4, 3) and B (8, −6)
`AB = sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2)`
= `sqrt((8 + 4)^2 + (-6 - 3)^2)`
= `sqrt(144 + 81)`
= `sqrt(225)`
= 15 units
ii. Let P be the point, which divides AB on the x-axis in the ratio k : 1.
Therefore, y-co-ordinate of P = 0.
`=> (-6k + 3)/(k + 1) = 0`
`=> -6k + 3 = 0`
`=> k = 1/2`
∴ Required ratio is 1 : 2.
APPEARS IN
RELATED QUESTIONS
Find the coordinates of the point which divides the line segment joining the points (6, 3) and (– 4, 5) in the ratio 3 : 2 internally.
Find the coordinates of the centroid of a triangle whose vertices are (–1, 0), (5, –2) and (8, 2)
Find the coordinates of the point which divides the join of (–1, 7) and (4, –3) in the ratio 2 : 3.
Find the area of a rhombus if its vertices are (3, 0), (4, 5), (− 1, 4) and (− 2, −1) taken in order.
[Hint: Area of a rhombus = `1/2` (product of its diagonals)]
Find the length of the medians of a ΔABC having vertices at A(0, -1), B(2, 1) and C(0, 3).
P is a point on the line joining A(4, 3) and B(–2, 6) such that 5AP = 2BP. Find the co-ordinates of P.
Show that the line segment joining the points (–5, 8) and (10, −4) is trisected by the co-ordinate axes.
The points A, B and C divides the line segment MN in four equal parts. The coordinates of Mand N are (-1, 10) and (7, -2) respectively. Find the coordinates of A, B and C.
Find the ratio in which the line segment joining A (2, -3) and B(S, 6) i~ divided by the x-axis.
What is the ratio in which the line segment joining (2, -3) and (5, 6) is divided by x-axis?
