Advertisements
Advertisements
प्रश्न
Name the type of quadrilateral formed, if any, by the following point, and give reasons for your answer:
(4, 5), (7, 6), (4, 3), (1, 2)
उत्तर
Let the points (4, 5), (7, 6), (4, 3), and (1, 2) be representing the vertices A, B, C, and D of the given quadrilateral respectively.
∴ AB = `sqrt((4-7)^2+(5-6)^2)`
= `sqrt((-3)^2+(-1)^2)`
= `sqrt(9+1)`
= `sqrt10`
BC = `sqrt((7-4)^2+(6-3)^2)`
= `sqrt((3)^2+(3)^2)`
= `sqrt(9+9)`
= `sqrt18`
CD = `sqrt((4-1)^2+(3-2)^2)`
= `sqrt((3)^2+(1)^2)`
= `sqrt(9+1)`
= `sqrt10`
AD = `sqrt((4-1)^2+(5-2)^2)`
= `sqrt((3)^2+(3)^2)`
= `sqrt(9+9)`
= `sqrt18`
Diagonal AC = `sqrt((4-4)^2+(5-3)^2)`
= `sqrt((0)^2+(2)^2)`
= `sqrt(0+4)`
= 2
Diagonal CD = `sqrt((7-1)^2 + (6-2)^2)`
= `sqrt((6)^2+(4)^2)`
= `sqrt(36+16)`
= `sqrt52`
= `13sqrt2`
It can be observed that opposite sides of this quadrilateral are of the same length. However, the diagonals are of different lengths. Therefore, the given points are the vertices of a parallelogram.
APPEARS IN
संबंधित प्रश्न
If A(5, 2), B(2, −2) and C(−2, t) are the vertices of a right angled triangle with ∠B = 90°, then find the value of t.
Find the distance between two points
(i) P(–6, 7) and Q(–1, –5)
(ii) R(a + b, a – b) and S(a – b, –a – b)
(iii) `A(at_1^2,2at_1)" and " B(at_2^2,2at_2)`
Name the type of quadrilateral formed, if any, by the following point, and give reasons for your answer:
(−3, 5), (3, 1), (0, 3), (−1, −4)
Find the distance between the following pair of points:
(a+b, b+c) and (a-b, c-b)
The length of a line segment is of 10 units and the coordinates of one end-point are (2, -3). If the abscissa of the other end is 10, find the ordinate of the other end.
A(–8, 0), B(0, 16) and C(0, 0) are the vertices of a triangle ABC. Point P lies on AB and Q lies on AC such that AP : PB = 3 : 5 and AQ : QC = 3 : 5. Show that : PQ = `3/8` BC.
Find x if distance between points L(x, 7) and M(1, 15) is 10.
Find the distance between the following pairs of point in the coordinate plane :
(7 , -7) and (2 , 5)
Find the coordinate of O , the centre of a circle passing through A (8 , 12) , B (11 , 3), and C (0 , 14). Also , find its radius.
Find the distance between the origin and the point:
(8, -15)
Give the relation that must exist between x and y so that (x, y) is equidistant from (6, -1) and (2, 3).
By using the distance formula prove that each of the following sets of points are the vertices of a right angled triangle.
(i) (6, 2), (3, -1) and (- 2, 4)
(ii) (-2, 2), (8, -2) and (-4, -3).
Show that the points (a, a), (-a, -a) and `(-asqrt(3), asqrt(3))` are the vertices of an equilateral triangle.
If the distance between point L(x, 7) and point M(1, 15) is 10, then find the value of x
Show that the points (0, –1), (8, 3), (6, 7) and (– 2, 3) are vertices of a rectangle.
The coordinates of the point which is equidistant from the three vertices of the ΔAOB as shown in the figure is ______.
If the distance between the points (4, P) and (1, 0) is 5, then the value of p is ______.
The distance of the point (α, β) from the origin is ______.
Ayush starts walking from his house to office. Instead of going to the office directly, he goes to a bank first, from there to his daughter’s school and then reaches the office. What is the extra distance travelled by Ayush in reaching his office? (Assume that all distances covered are in straight lines). If the house is situated at (2, 4), bank at (5, 8), school at (13, 14) and office at (13, 26) and coordinates are in km.
