Advertisements
Advertisements
Question
Show that the following points are the vertices of a rectangle
A (0,-4), B(6,2), C(3,5) and D(-3,-1)
Advertisements
Solution
The given points are A (0,-4), B(6,2), C(3,5) and D(-3,-1).
`AB = sqrt((6-0)^2 +{2-(-4)}^2) = sqrt((6)^2 +(6)^2) = sqrt(36+36) = sqrt(72) = 6 sqrt(2) units`
`BC = sqrt(( 3-6)^2 + (5-2)^2) = sqrt((-3)^2 +(3)^2) = sqrt(9+9) = sqrt(18) = 3 sqrt(2) units`
` CD = sqrt((-3-3)^2 +(-1-5)^2) = sqrt((-6)^2 +(-6)^2) = sqrt(36+36) = sqrt(72) = 6 sqrt(2) units`
` AD = sqrt((-3-0)^2 + { -1-(-4)}^2) = sqrt((-3)^2 +(3)^2) = sqrt(9+9) = sqrt(18) = 3 sqrt(2) units`
` Thus , AB =CD = sqrt(10) " units and " BC = AD = sqrt(5) units`
`Also , AC = sqrt((3-0)^2 +{ 5-(-4)}^2) = sqrt((3)^2 +(9)^2 )= sqrt(9+81) = sqrt(90) = 3 sqrt(10) units`
`BD = sqrt((-3-6)^2 +(-1-2)^2) = sqrt((-9)^2 +(-3)^2) = sqrt(81+9) = sqrt(90) = 3 sqrt(10) units`
Also, diagonal AC = diagonal BD
Hence, the given points from a rectangle
APPEARS IN
RELATED QUESTIONS
Find the third vertex of a triangle, if two of its vertices are at (−3, 1) and (0, −2) and the centroid is at the origin.
A (3, 2) and B (−2, 1) are two vertices of a triangle ABC whose centroid G has the coordinates `(5/3,-1/3)`Find the coordinates of the third vertex C of the triangle.
In what ratio does the point (−4, 6) divide the line segment joining the points A(−6, 10) and B(3,−8)?
If the point P (2,2) is equidistant from the points A ( -2,K ) and B( -2K , -3) , find k. Also, find the length of AP.
Find the ratio in which the point (-1, y) lying on the line segment joining points A(-3, 10) and (6, -8) divides it. Also, find the value of y.
Find the coordinates of the points of trisection of the line segment joining the points (3, –2) and (–3, –4) ?
The abscissa of any point on y-axis is
If (a,b) is the mid-point of the line segment joining the points A (10, - 6) , B (k,4) and a - 2b = 18 , find the value of k and the distance AB.
Find the value of k if points A(k, 3), B(6, −2) and C(−3, 4) are collinear.
If the centroid of the triangle formed by points P (a, b), Q(b, c) and R (c, a) is at the origin, what is the value of a + b + c?
The distance between the points (a cos 25°, 0) and (0, a cos 65°) is
The area of the triangle formed by (a, b + c), (b, c + a) and (c, a + b)
If the area of the triangle formed by the points (x, 2x), (−2, 6) and (3, 1) is 5 square units , then x =
If A(x, 2), B(−3, −4) and C(7, −5) are collinear, then the value of x is
If segment AB is parallel Y-axis and coordinates of A are (1, 3), then the coordinates of B are ______
If point P is midpoint of segment joining point A(– 4, 2) and point B(6, 2), then the coordinates of P are ______
Abscissa of a point is positive in ______.
Which of the points P(0, 3), Q(1, 0), R(0, –1), S(–5, 0), T(1, 2) do not lie on the x-axis?
In which quadrant, does the abscissa, and ordinate of a point have the same sign?
In which ratio the y-axis divides the line segment joining the points (5, – 6) and (–1, – 4)?
