Advertisements
Advertisements
Question
Point P(5, –3) is one of the two points of trisection of the line segment joining the points A(7, –2) and B(1, –5).
Options
True
False
Solution
This statement is True.
Explanation:
Let P(5, –3) divides the line segment joining the points A(7, –2) and B(1, –5) in the ratio k : 1 internally.
By section formula, the coordinate of point P will be
`((k(1) + (1)(7))/(k + 1), (k(-5) + 1(-2))/(k + 1))`
i.e., `((k + 7)/(k + 1), (-5k - 2)/(k + 1))`
Now, (5, –3) = `((k + 7)/(k + 1), (-5k - 2)/(k + 1))`
⇒ `(k + 7)/(k + 1)` = 5
⇒ k + 7 = 5k + 5
⇒ – 4k = – 2
∴ k = `1/2`
So the point P divides the line segment AB in ratio 1 : 2.
Hence, point P in the point of trisection of AB.
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 length of the medians of a ΔABC having vertices at A(0, -1), B(2, 1) and C(0, 3).
A (2, 5), B (–1, 2) and C (5, 8) are the co-ordinates of the vertices of the triangle ABC. Points P and Q lie on AB and AC respectively, such that : AP : PB = AQ : QC = 1 : 2.
- Calculate the co-ordinates of P and Q.
- Show that : `PQ = 1/3 BC`.
In what ratio is the line joining A(0, 3) and B(4, –1) divided by the x-axis? Write the co-ordinates of the point where AB intersects the x-axis.
If point P(1, 1) divide segment joining point A and point B(–1, –1) in the ratio 5 : 2, then the coordinates of A are ______
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.
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 ______.
Find the coordinates of the point R on the line segment joining the points P(–1, 3) and Q(2, 5) such that PR = `3/5` PQ.
The points A(x1, y1), B(x2, y2) and C(x3, y3) are the vertices of ∆ABC. Find the coordinates of the point P on AD such that AP : PD = 2 : 1
Find the ratio in which the line segment joining the points A(6, 3) and B(–2, –5) is divided by x-axis.
