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प्रश्न
A line intersects y-axis and x-axis at point P and Q, respectively. If R(2, 5) is the mid-point of line segment PQ, them find the coordinates of P and Q.
उत्तर
Let P point be (0, y)
and Q point be (x, 0)
Since, on y-axis, x = 0 and on x-axis, y = 0
Let coordinates of point P be (0, y)
and coordinates of point Q be (x, 0)
Since, mid-point of points (x1, y1) and (x2, y2) is
`((x_1 + x_2)/2, (y_1 + y_2)/2)`
∴ 2 = `(0 + x)/2 \implies` x = 4
and 5 = `(y + 0)/2 \implies` y = 10
∴ coordinates of P = (0, 10)
and coordinates of Q = (4, 0)
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संबंधित प्रश्न
The line segment joining the points (3, -4) and (1, 2) is trisected at the points P and Q. If the coordinates of P and Q are (p, -2) and (5/3, q) respectively. Find the values of p and q.
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Find the co-ordinates of the centroid of a triangle ABC whose vertices are: A(–1, 3), B(1, –1) and C(5, 1).
If `P(a/3, 4)` is the mid-point of the line segment joining the points Q(– 6, 5) and R(– 2, 3), then the value of a is ______.
If the points A(1, 2), O(0, 0), C(a, b) are collinear, then ______.
In what ratio does the x-axis divide the line segment joining the points (– 4, – 6) and (–1, 7)? Find the coordinates of the point of division.
The points A(x1, y1), B(x2, y2) and C(x3, y3) are the vertices of ∆ABC. What are the coordinates of the centroid of the triangle ABC?
Complete the following activity to find the coordinates of point P which divides seg AB in the ratio 3:1 where A(4, – 3) and B(8, 5).
Activity:
∴ By section formula,
∴ x = `("m"x_2 + "n"x_1)/square`,
∴ x = `(3 xx 8 + 1 xx 4)/(3 + 1)`,
= `(square + 4)/4`,
∴ x = `square`,
∴ y = `square/("m" + "n")`
∴ y = `(3 xx 5 + 1 xx (-3))/(3 + 1)`
= `(square - 3)/4`
∴ y = `square`
