Advertisements
Advertisements
प्रश्न
If the distance between the points (3, 0) and (0, y) is 5 units and y is positive. then what is the value of y?
उत्तर
It is given that distance between P (3, 0) and Q (0 , y) is 5.
In general, the distance between A`(x_1 , y_1 ) " and B "(x_2 , y_12)` is given by,
`AB^2 = (x_2 - x_1) ^2 + ( y_2 - y_1)^2`
So,
`5^2 = (0 -3)^2 + ( y - 0)^2`
On further simplification,
`y^2 = 16`
` y = +-4`
We will neglect the negative value. So,
y = 4
APPEARS IN
संबंधित प्रश्न
Which point on the y-axis is equidistant from (2, 3) and (−4, 1)?
If two opposite vertices of a square are (5, 4) and (1, −6), find the coordinates of its remaining two vertices.
Show that the points (−3, 2), (−5,−5), (2, −3) and (4, 4) are the vertices of a rhombus. Find the area of this rhombus.
If the points A (a, -11), B (5, b), C (2, 15) and D (1, 1) are the vertices of a parallelogram ABCD, find the values of a and b.
Find the points on the y-axis which is equidistant form the points A(6,5) and B(- 4,3)
Show that the following points are the vertices of a square:
(i) A (3,2), B(0,5), C(-3,2) and D(0,-1)
Point A lies on the line segment PQ joining P(6, -6) and Q(-4, -1) in such a way that `(PA)/( PQ)=2/5` . If that point A also lies on the line 3x + k( y + 1 ) = 0, find the value of k.
If the vertices of ΔABC be A(1, -3) B(4, p) and C(-9, 7) and its area is 15 square units, find the values of p
If the points A(4,3) and B( x,5) lie on the circle with center O(2,3 ) find the value of x .
Show that the points (−4, −1), (−2, −4) (4, 0) and (2, 3) are the vertices points of a rectangle.
Write the ratio in which the line segment joining points (2, 3) and (3, −2) is divided by X axis.
What is the distance between the points \[A\left( \sin\theta - \cos\theta, 0 \right)\] and \[B\left( 0, \sin\theta + \cos\theta \right)\] ?
If the area of the triangle formed by the points (x, 2x), (−2, 6) and (3, 1) is 5 square units , then x =
If the points P (x, y) is equidistant from A (5, 1) and B (−1, 5), then
Which of the points P(-1, 1), Q(3, - 4), R(1, -1), S (-2, -3), T(-4, 4) lie in the fourth quadrant?
The line segment joining the points (3, -1) and (-6, 5) is trisected. The coordinates of point of trisection are ______.
Point P(– 4, 2) lies on the line segment joining the points A(– 4, 6) and B(– 4, – 6).
Point (–10, 0) lies ______.
If the coordinates of the two points are P(–2, 3) and Q(–3, 5), then (abscissa of P) – (abscissa of Q) is ______.
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?
