Advertisements
Advertisements
Question
Show that the following points are the vertices of a square:
(i) A (3,2), B(0,5), C(-3,2) and D(0,-1)
Advertisements
Solution
The given points are A (3,2), B(0,5), C(-3,2) and D(0,-1).
`AB = sqrt((0-3)^2 +(5-2)^2 ) = sqrt((-3)^2 +(3)^2 ) = sqrt(9+9) = sqrt(18) = 3 sqrt(2) units `
`BC= sqrt((-3-0)^2 + (2-5)^2) = sqrt((-3)^2 +(3)^2) = sqrt(9+9) = sqrt(18) = 3 sqrt(2) ` units
`CD = sqrt((0+3)^2 + (-1-2)^2) = sqrt((3)^2 +(-3)^2) = sqrt(9+9) = sqrt(18) = 3 sqrt(2) units`
`DA = sqrt((0-3)^2 +(-1-2)^2) = sqrt((-3)^2+(-3)^2) = sqrt(9+9) =sqrt(18) = 3sqrt(2) units`
Therefore`AB =BC=CD=DA=3 sqrt(2) units`
Also, `AC = sqrt((-3-3)^2 +(2-2)^2) = sqrt((-6)^2 +(0)^2) = sqrt(36) = 6 units`
`BD = sqrt((0-0)^2 + (-1-5)^2) = sqrt((0)^2 +(-6)^2 )= sqrt(36) = 6 units`
Thus, diagonal AC = diagonal BD
Therefore, the given points from a square.
APPEARS IN
RELATED QUESTIONS
Find the value of k, if the point P (0, 2) is equidistant from (3, k) and (k, 5).
In what ratio does the point (−4, 6) divide the line segment joining the points A(−6, 10) and B(3,−8)?
Show that the following points are the vertices of a rectangle.
A (2, -2), B(14,10), C(11,13) and D(-1,1)
Find the area of quadrilateral ABCD whose vertices are A(-3, -1), B(-2,-4) C(4,-1) and D(3,4)
Find the ratio in which the line segment joining the points A (3, 8) and B (–9, 3) is divided by the Y– axis.
If `P(a/2,4)`is the mid-point of the line-segment joining the points A (−6, 5) and B(−2, 3), then the value of a is
Mark the correct alternative in each of the following:
The point of intersect of the coordinate axes is
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.
Find the centroid of the triangle whose vertices is (−2, 3) (2, −1) (4, 0) .
In \[∆\] ABC , the coordinates of vertex A are (0, - 1) and D (1,0) and E(0,10) respectively the mid-points of the sides AB and AC . If F is the mid-points of the side BC , find the area of \[∆\] DEF.
What is the distance between the points A (c, 0) and B (0, −c)?
In Fig. 14.46, the area of ΔABC (in square units) is
If A(4, 9), B(2, 3) and C(6, 5) are the vertices of ∆ABC, then the length of median through C is
If A(x, 2), B(−3, −4) and C(7, −5) are collinear, then the value of x is
Write the X-coordinate and Y-coordinate of point P(– 5, 4)
Point P(– 4, 2) lies on the line segment joining the points A(– 4, 6) and B(– 4, – 6).
Abscissa of a point is positive in ______.
Find the coordinates of the point whose ordinate is – 4 and which lies on y-axis.
The distance of the point (–6, 8) from x-axis is ______.
The distance of the point (3, 5) from x-axis (in units) is ______.
