Advertisements
Advertisements
प्रश्न
Show that the following points are the vertices of a rectangle.
A (2, -2), B(14,10), C(11,13) and D(-1,1)
Advertisements
उत्तर
The given points are A (2, -2), B(14,10), C(11,13) and D(-1,1).
`AB = sqrt((14-2)^2 +{10-(-2)}^2) = sqrt((12)^2 +(12)^2) =sqrt(144+144) = sqrt(288) =12 sqrt(2) units`
`BC = sqrt(( 11-14)^2 +(13-10)^2 ) = sqrt((-3)^2 +(3)^2) = sqrt(9+9) = sqrt(18) = 3 sqrt(2) units`
` CD = sqrt((-1-11)^2 +(1-13)^2) = sqrt((-12)^2 +(-12)^2) = sqrt(144+144) = sqrt(288) = 12 sqrt(2) units`
`AD = sqrt((-1-2)^2 +{1-(-2)}^2) = sqrt((-3)^2 +(3)^2) = sqrt(9+9) = sqrt(18) =3 sqrt(2) units`
`Thus AB =CD = 12 sqrt(2) "units and " BC =AD = 3 sqrt(2) units`
Also ,
`AC = sqrt((11-2)^2 +{ 13-(-2)}^2) = sqrt((9)^2 +(15)^2) = sqrt(81+225) = sqrt(306) = 3 sqrt(34) units `
` BD = sqrt((-1-14)^2 +(1-10)^2) = sqrt((-15)^2 +(-9)^2) = sqrt(81+225) = sqrt(306) =3 sqrt(34) units`
Also, diagonal AC = diagonal BD
Hence, the given points from a rectangle
APPEARS IN
संबंधित प्रश्न
(Street Plan): A city has two main roads which cross each other at the centre of the city. These two roads are along the North-South direction and East-West direction.
All the other streets of the city run parallel to these roads and are 200 m apart. There are 5 streets in each direction. Using 1cm = 200 m, draw a model of the city on your notebook. Represent the roads/streets by single lines.
There are many cross- streets in your model. A particular cross-street is made by two streets, one running in the North - South direction and another in the East - West direction. Each cross street is referred to in the following manner : If the 2nd street running in the North - South direction and 5th in the East - West direction meet at some crossing, then we will call this cross-street (2, 5). Using this convention, find:
- how many cross - streets can be referred to as (4, 3).
- how many cross - streets can be referred to as (3, 4).
Find the equation of the perpendicular bisector of the line segment joining points (7, 1) and (3,5).
The line joining the points (2, 1) and (5, −8) is trisected at the points P and Q. If point P lies on the line 2x − y + k = 0. Find the value of k.
Find the co-ordinates of the point which divides the join of A(-5, 11) and B(4,-7) in the ratio 7 : 2
Find the area of the triangle formed by joining the midpoints of the sides of the triangle whose vertices are A(2,1) B(4,3) and C(2,5)
If the point P(k - 1, 2) is equidistant from the points A(3, k) and B(k, 5), find the value of k.
Find the point on x-axis which is equidistant from points A(-1,0) and B(5,0)
Show that the points (−2, 3), (8, 3) and (6, 7) are the vertices of a right triangle ?
The abscissa and ordinate of the origin are
Points (−4, 0) and (7, 0) lie
If the point P(x, 3) is equidistant from the point A(7, −1) and B(6, 8), then find the value of x and find the distance AP.
If the point \[C \left( - 1, 2 \right)\] divides internally the line segment joining the points A (2, 5) and B( x, y ) in the ratio 3 : 4 , find the value of x2 + y2 .
A line segment is of length 10 units. If the coordinates of its one end are (2, −3) and the abscissa of the other end is 10, then its ordinate is
If the area of the triangle formed by the points (x, 2x), (−2, 6) and (3, 1) is 5 square units , then x =
The line segment joining points (−3, −4), and (1, −2) is divided by y-axis in the ratio.
What is the nature of the line which includes the points (-5, 5), (6, 5), (-3, 5), (0, 5)?
Write the equations of the x-axis and y-axis.
Find the coordinates of the point of intersection of the graph of the equation x = 2 and y = – 3
What are the coordinates of origin?
Students of a school are standing in rows and columns in their playground for a drill practice. A, B, C and D are the positions of four students as shown in figure. Is it possible to place Jaspal in the drill in such a way that he is equidistant from each of the four students A, B, C and D? If so, what should be his position?
