Advertisements
Advertisements
प्रश्न
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.
उत्तर
According to the question,
Given that,
PR = `3/5`PQ
⇒ `("PQ")/("PR") = 5/3`
⇒ `("PR" + "RQ")/("PR") = 5/3`
⇒ `1 + ("RQ")/("PR") = 5/3`
⇒ `("PQ")/("PR") = 5/3 - 1 = 2/3`
∴ RQ : PR = 2 : 3
or PR : RQ = 3 : 2
Suppose, R(x, y) be the point which divides the line segment joining the points P(–1, 3) and Q(2, 5) in the ratio 3 : 2
∴ (x, y) = `{(3(2) + 2(-1))/(3 + 2), (3(5) + 2(3))/(3 + 2)}` ...`[∵ "By internal section formula", {(m_2x_1 + m_1x_2)/(m_1 + m_2), (m_2y_1 + m_1y_2)/(m_1 + m_2)}]`
= `((6 - 2)/5, (15 + 6)/5)`
= `(4/5, 21/5)`
Hence, the required coordinates of the point R is `(4/5, 21/5)`.
APPEARS IN
संबंधित प्रश्न
Find the ratio in which y-axis divides the line segment joining the points A(5, –6) and B(–1, –4). Also find the coordinates of the point of division.
Prove that (4, – 1), (6, 0), (7, 2) and (5, 1) are the vertices of a rhombus. Is it a square?
Find the lengths of the medians of a ΔABC having vertices at A(5, 1), B(1, 5), and C(-3, -1).
Show that the mid-point of the line segment joining the points (5, 7) and (3, 9) is also the mid-point of the line segment joining the points (8, 6) and (0, 10).
In what ratio is the join of (4, 3) and (2, –6) divided by the x-axis? Also, find the co-ordinates of the point of intersection.
Calculate the ratio in which the line joining the points (–3, –1) and (5, 7) is divided by the line x = 2. Also, find the co-ordinates of the point of intersection.
The origin o (0, O), P (-6, 9) and Q (12, -3) are vertices of triangle OPQ. Point M divides OP in the ratio 1: 2 and point N divides OQ in the ratio 1: 2. Find the coordinates of points M and N. Also, show that 3MN = PQ.
Show that the line segment joining the points (-3, 10) and (6, -5) is trisected by the coordinates axis.
In what ratio is the line joining (2, -1) and (-5, 6) divided by the y axis ?
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.
