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प्रश्न
In the following figure line APB meets the X-axis at A, Y-axis at B. P is the point (4, -2) and AP: PB = 1: 2. Write down the coordinates of A and B.
उत्तर
Let (x, 0) and (0, y) be the coordinates of A and B respectively.
Point P divides AB in the ratio of 1: 2
So coordinates of P
4 = `(1 xx 0 + 2 xx x )/(1 + 2)`
⇒ 2x = 4 x 3
⇒ x = 6
Also -2 = `(2 xx 0 + 1 xx y)/(1 + 2)`
⇒ -6 = y
⇒ y = -6.
Hence, the coordinates of A and B are (-6, 0) and (0, 6) respectively.
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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.
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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.
Calculate the ratio in which the line joining A(-4,2) and B(3,6) is divided by point p(x,3). Also, find x
Find the ratio in which the line 2x + y = 4 divides the line segment joining the point P(2, –2) and Q(3, 7).
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).
The line segment joining A (2, 3) and B (6, – 5) is intersected by the X axis at the point K. Write the ordinate of the point K. Hence find the ratio in which K divides AB.
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