Advertisements
Advertisements
प्रश्न
Find the area of a rhombus if its vertices are (3, 0), (4, 5), (− 1, 4) and (− 2, −1) taken in order.
[Hint: Area of a rhombus = `1/2` (product of its diagonals)]
उत्तर
Let (3, 0), (4, 5), (−1, 4) and (−2, −1) are the vertices A, B, C, D of a rhombus ABCD.
Length of diagonal AC = `sqrt([3-(-1)]^2 + (0-4)^2)`
= `sqrt((-4)^2 + (4)^2)`
= `sqrt (16 + 16)`
= `4sqrt2`
Length of diagonal BD = `sqrt([4-(-2)]^2+[5-(-1)]^2)`
= `sqrt((-6)^2 + (-6)^2)`
= `sqrt(36+36) `
= `6sqrt2`
Therefore, area of rhombus ABCD = `1/2xx("Product of diagonals")`
= `1/2xx"AC"xx"BD"`
= `1/2xx4sqrt2xx6sqrt2`
= `1/2xx2xx4xx6`
= 24 square units
APPEARS IN
संबंधित प्रश्न
Find the ratio in which y-axis divides the line segment joining the points A(5, –6) and B(–1, –4). Also find the coordinates of the point of division.
Find the ratio in which the line segment joining A (1, −5) and B (−4, 5) is divided by the x-axis. Also, find the coordinates of the point of division.
If A and B are (−2, −2) and (2, −4), respectively, find the coordinates of P such that `"AP" = 3/7 "AB"` and P lies on the line segment AB.
If two vertices of a parallelogram are (3, 2) (-1, 0) and the diagonals cut at (2, -5), find the other vertices of the parallelogram.
Find the lengths of the medians of a ΔABC having vertices at A(5, 1), B(1, 5), and C(-3, -1).
The line segment joining the points (3, -4) and (1, 2) is trisected at the points P and Q. If the coordinates of P and Q are (p, -2) and (5/3, q) respectively. Find the values of p and q.
If A = (−4, 3) and B = (8, −6)
- Find the length of AB.
- In what ratio is the line joining A and B, divided by the x-axis?
Find the ratio in which the y-axis divides the line segment joining the points (−4, − 6) and (10, 12). Also find the coordinates of the point of division ?
In Figure 2, P (5, −3) and Q (3, y) are the points of trisection of the line segment joining A (7, −2) and B (1, −5). Then y equals
Find the coordinate of a point P which divides the line segment joining :
D(-7, 9) and E( 15, -2) in the ratio 4:7.
Find the ratio in which the line x = -2 divides the line segment joining (-6, -1) and (1, 6). Find the coordinates of the point of intersection.
B is a point on the line segment AC. The coordinates of A and B are (2, 5) and (1, 0). If AC= 3 AB, find the coordinates of C.
If point P(1, 1) divide segment joining point A and point B(–1, –1) in the ratio 5 : 2, then the coordinates of A are ______
The point which divides the line segment joining the points (7, –6) and (3, 4) in ratio 1 : 2 internally lies in the ______.
The fourth vertex D of a parallelogram ABCD, whose three vertices are A(–2, 3), B(6, 7) and C(8, 3), is ______.
In what ratio does the x-axis divide the line segment joining the points (– 4, – 6) and (–1, 7)? Find the coordinates of the point of division.
Find the ratio in which the line 2x + 3y – 5 = 0 divides the line segment joining the points (8, –9) and (2, 1). Also find the coordinates of the point of division.
If the points A(1, –2), B(2, 3) C(a, 2) and D(– 4, –3) form a parallelogram, find the value of a and height of the parallelogram taking AB as base.
Find the co-ordinates of the points of trisection of the line segment joining the points (5, 3) and (4, 5).
