Advertisements
Advertisements
Question
What type of a quadrilateral do the points A(2, –2), B(7, 3), C(11, –1) and D(6, –6) taken in that order, form?
Advertisements
Solution
The points are A(2, –2), B(7, 3), C(11, –1) and D(6, –6)
Using distance formula,
d = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2`
AB = `sqrt((7 - 2)^2 + (3 + 2)^2`
= `sqrt((5)^2 + (5)^2`
= `sqrt(25 + 25)`
= `sqrt(50)`
= 5`sqrt(2)`
BC = `sqrt((11 - 7)^2 + (-1 - 3)^2`
= `sqrt((4)^2 + (-4)^2`
= `sqrt(16 + 16)`
= `sqrt(32)`
= `4sqrt(2)`
CD = `sqrt((6 - 11)^2 + (-6 + 1)^2`
= `sqrt((-5)^2 + (-5)^2`
= `sqrt(25 + 25)`
= `sqrt(50)`
= `5sqrt(2)`
DA = `sqrt((2 - 6)^2 + (-2 + 6)^2`
= `sqrt((-4)^2 + (4)^2`
= `sqrt(16 + 16)`
= `sqrt(32)`
= `4sqrt(2)`
Finding diagonals AC and BD, we get,
AC = `sqrt((11 - 2)^2 + (-1 + 2)^2`
= `sqrt((9)^2 + (1)^2`
= `sqrt(81 + 1)`
= `sqrt(82)`
And BD = `sqrt((6 - 7)^2 + (-6 - 3)^2`
= `sqrt((-1)^2 + (-9)^2`
= `sqrt(1 + 81)`
= `sqrt(82)`
The quadrilateral formed is rectangle.
APPEARS IN
RELATED QUESTIONS
Find the value of x, if the distance between the points (x, – 1) and (3, 2) is 5.
Find the distance between the points (0, 0) and (36, 15). Can you now find the distance between the two towns A and B discussed in Section 7.2.
Find the co-ordinates of points of trisection of the line segment joining the point (6, –9) and the origin.
Using the distance formula, show that the given points are collinear:
(1, -1), (5, 2) and (9, 5)
The long and short hands of a clock are 6 cm and 4 cm long respectively. Find the sum of the distances travelled by their tips in 24 hours. (Use π = 3.14) ?
Find the distance between the following pair of point.
T(–3, 6), R(9, –10)
Determine whether the point is collinear.
R(0, 3), D(2, 1), S(3, –1)
Find x if distance between points L(x, 7) and M(1, 15) is 10.
Show that the ▢PQRS formed by P(2, 1), Q(–1, 3), R(–5, –3) and S(–2, –5) is a rectangle.
Find the distance between the following pair of point in the coordinate plane :
(5 , -2) and (1 , 5)
Prove that the following set of point is collinear :
(5 , 5),(3 , 4),(-7 , -1)
x (1,2),Y (3, -4) and z (5,-6) are the vertices of a triangle . Find the circumcentre and the circumradius of the triangle.
Prove that the points (0 , -4) , (6 , 2) , (3 , 5) and (-3 , -1) are the vertices of a rectangle.
From the given number line, find d(A, B):
Points A (-3, -2), B (-6, a), C (-3, -4) and D (0, -1) are the vertices of quadrilateral ABCD; find a if 'a' is negative and AB = CD.
Calculate the distance between A (7, 3) and B on the x-axis whose abscissa is 11.
Find the distance of the following points from origin.
(a+b, a-b)
Show that the quadrilateral with vertices (3, 2), (0, 5), (- 3, 2) and (0, -1) is a square.
The distance between point P(2, 2) and Q(5, x) is 5 cm, then the value of x = ______.
The centre of a circle is (2a, a – 7). Find the values of a if the circle passes through the point (11, – 9) and has diameter `10sqrt(2)` units.
