Advertisements
Advertisements
प्रश्न
Find the coordinates of the midpoints of the line segment joining
A(3,0) and B(-5, 4)
Advertisements
उत्तर
The given points are A(3,0) and B(-5, 4)
Let ( x,y) be the midpoint of AB. Then :
` x= (x_1 +x_2)/2 , y = (y_1+y_2)/2`
` ⇒ x = (3+(-5))/2 , y = (0+4) /2 `
`⇒ x =(-2)/2 , y = 4/2 `
⇒ x = -1 , y=2
Therefore, (-1,2) are the coordinates of midpoint of AB.
APPEARS IN
संबंधित प्रश्न
On which axis do the following points lie?
Q(0, -2)
Show that the points A(5, 6), B(1, 5), C(2, 1) and D(6,2) are the vertices of a square.
The line segment joining the points P(3, 3) and Q(6, -6) is trisected at the points A and B such that Ais nearer to P. If A also lies on the line given by 2x + y + k = 0, find the value of k.
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.
Show that the points A(6,1), B(8,2), C(9,4) and D(7,3) are the vertices of a rhombus. Find its area.
`"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).`
Find the point on x-axis which is equidistant from points A(-1,0) and B(5,0)
If the points A (2,3), B (4,k ) and C (6,-3) are collinear, find the value of k.
Show that the points (−2, 3), (8, 3) and (6, 7) are the vertices of a right triangle ?
Find the coordinates of the circumcentre of a triangle whose vertices are (–3, 1), (0, –2) and (1, 3).
Show that A(-4, -7), B(-1, 2), C(8, 5) and D(5, -4) are the vertices of a
rhombus ABCD.
The points \[A \left( x_1 , y_1 \right) , B\left( x_2 , y_2 \right) , C\left( x_3 , y_3 \right)\] are the vertices of ΔABC .
(i) The median from A meets BC at D . Find the coordinates of the point D.
(ii) Find the coordinates of the point P on AD such that AP : PD = 2 : 1.
(iii) Find the points of coordinates Q and R on medians BE and CF respectively such thatBQ : QE = 2 : 1 and CR : RF = 2 : 1.
(iv) What are the coordinates of the centropid of the triangle ABC ?
Write the ratio in which the line segment joining points (2, 3) and (3, −2) is divided by X axis.
If the line segment joining the points (3, −4), and (1, 2) is trisected at points P (a, −2) and Q \[\left( \frac{5}{3}, b \right)\] , Then,
What is the form of co-ordinates of a point on the X-axis?
What is the nature of the line which includes the points (-5, 5), (6, 5), (-3, 5), (0, 5)?
If the coordinates of the two points are P(–2, 3) and Q(–3, 5), then (abscissa of P) – (abscissa of Q) is ______.
Find the coordinates of the point which lies on x and y axes both.
If the vertices of a parallelogram PQRS taken in order are P(3, 4), Q(–2, 3) and R(–3, –2), then the coordinates of its fourth vertex S are ______.
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?
