Advertisements
Advertisements
प्रश्न
In what ratio is the line segment joining the points A(-2, -3) and B(3,7) divided by the yaxis? Also, find the coordinates of the point of division.
Advertisements
उत्तर
Let AB be divided by the x-axis in the ratio :1 k at the point P.
Then, by section formula the coordination of P are
`p = ((3k-2)/(k+1) , (7k-3)/(k+1))`
But P lies on the y-axis; so, its abscissa is 0.
Therefore , `(3k-2)/(k+1) = 0`
`⇒ 3k-2 = 0 ⇒3k=2 ⇒ k = 2/3 ⇒ k = 2/3 `
Therefore, the required ratio is `2/3:1`which is same as 2 : 3
Thus, the x-axis divides the line AB in the ratio 2 : 3 at the point P.
Applying `k= 2/3,` we get the coordinates of point.
`p (0,(7k-3)/(k+1))`
`= p(0, (7xx2/3-3)/(2/3+1))`
`= p(0, ((14-9)/3)/((2+3)/3))`
`= p (0,5/5)`
= p(0,1)
Hence, the point of intersection of AB and the x-axis is P (0,1).
APPEARS IN
संबंधित प्रश्न
Prove that the points (−2, 5), (0, 1) and (2, −3) are collinear.
Which point on the y-axis is equidistant from (2, 3) and (−4, 1)?
Determine the ratio in which the straight line x - y - 2 = 0 divides the line segment
joining (3, -1) and (8, 9).
If A and B are (1, 4) and (5, 2) respectively, find the coordinates of P when AP/BP = 3/4.
`"Find the ratio in which the poin "p (3/4 , 5/12) " divides the line segment joining the points "A (1/2,3/2) and B (2,-5).`
If the points P (a,-11) , Q (5,b) ,R (2,15) and S (1,1). are the vertices of a parallelogram PQRS, find the values of a and b.
In what ratio does the point C (4,5) divides the join of A (2,3) and B (7,8) ?
Find the coordinates of circumcentre and radius of circumcircle of ∆ABC if A(7, 1), B(3, 5) and C(2, 0) are given.
Point P(x, 4) lies on the line segment joining the points A(−5, 8) and B(4, −10). Find the ratio in which point P divides the line segment AB. Also find the value of x.
Show that A (−3, 2), B (−5, −5), C (2,−3), and D (4, 4) are the vertices of a rhombus.
If R (x, y) is a point on the line segment joining the points P (a, b) and Q (b, a), then prove that x + y = a + b.
Find the value of k, if the points A (8, 1) B(3, −4) and C(2, k) are collinear.
If the points A(1, –2), B(2, 3) C(a, 2) and D(– 4, –3) form a parallelogram, find the value of a and height of the parallelogram taking AB as base.
If the centroid of the triangle formed by points P (a, b), Q(b, c) and R (c, a) is at the origin, what is the value of a + b + c?
If P (2, 6) is the mid-point of the line segment joining A(6, 5) and B(4, y), find y.
The distance of the point P(2, 3) from the x-axis is ______.
Find the coordinates of the point whose abscissa is 5 and which lies on x-axis.
Assertion (A): The ratio in which the line segment joining (2, -3) and (5, 6) internally divided by x-axis is 1:2.
Reason (R): as formula for the internal division is `((mx_2 + nx_1)/(m + n) , (my_2 + ny_1)/(m + n))`
A tiling or tessellation of a flat surface is the covering of a plane using one or more geometric shapes, called tiles, with no overlaps and no gaps. Historically, tessellations were used in ancient Rome and in Islamic art. You may find tessellation patterns on floors, walls, paintings etc. Shown below is a tiled floor in the archaeological Museum of Seville, made using squares, triangles and hexagons.
A craftsman thought of making a floor pattern after being inspired by the above design. To ensure accuracy in his work, he made the pattern on the Cartesian plane. He used regular octagons, squares and triangles for his floor tessellation pattern
Use the above figure to answer the questions that follow:
- What is the length of the line segment joining points B and F?
- The centre ‘Z’ of the figure will be the point of intersection of the diagonals of quadrilateral WXOP. Then what are the coordinates of Z?
- What are the coordinates of the point on y-axis equidistant from A and G?
OR
What is the area of Trapezium AFGH?
