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प्रश्न
Calculate the co-ordinates of the point P which divides the line segment joining: A (–4, 6) and B (3, –5) in the ratio 3 : 2
उत्तर
Let the co-ordinates of the point P be (x, y).
`x = (m_1x_2 + m_2x_1)/(m_1 + m_2)`
= `(3 xx 3 + 2 xx (-4))/(3 + 2)`
= `1/5`
`y = (m_1y_2 + m_2y_1)/(m_1 + m_2)`
= `(3 xx (-5) + 2 xx 6)/(3 + 2)`
= `(-3)/5`
Thus, the co-ordinates of point P are `(1/5, (-3)/5)`
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संबंधित प्रश्न
P(1, -2) is a point on the line segment A(3, -6) and B(x, y) such that AP : PB is equal to 2 : 3. Find the coordinates of B.
In what ratio is the line joining (2, –3) and (5, 6) divided by the x-axis?
In what ratio is the line joining (2, –4) and (–3, 6) divided by the y-axis?
In what ratio does the point (1, a) divide the join of (–1, 4) and (4, –1)? Also, find the value of a.
Find the ratio in which the line 2x + y = 4 divides the line segment joining the point P(2, –2) and Q(3, 7).
M is the mid-point of the line segment joining the points A(0, 4) and B(6, 0). M also divides the line segment OP in the ratio 1 : 3. Find :
- co-ordinates of M
- co-ordinates of P
- length of BP
A(–4, 2), B(0, 2) and C(–2, –4) are vertices of a triangle ABC. P, Q and R are mid-points of sides BC, CA and AB respectively. Show that the centroid of ΔPQR is the same as the centroid of ΔABC.
Find the image of the point A(5,3) under reflection in the point P(-1,3).
Determine the ratio in which the line 3x + y – 9 = 0 divides the line joining (1, 3) and (2, 7).
From the adjacent figure:
(i) Write the coordinates of the points A, B, and
(ii) Write the slope of the line AB.
(iii) Line through C, drawn parallel to AB, intersects Y-axis at D. Calculate the co-ordinates of D.
