Advertisements
Advertisements
प्रश्न
Show hat A(1,2), B(4,3),C(6,6) and D(3,5) are the vertices of a parallelogram. Show that ABCD is not rectangle.
Advertisements
उत्तर
The given vertices are A(1,2), B(4,3),C(6,6) and D(3,5) .
`AB = sqrt((1-4)^2+(2-3)^2) = sqrt((-3)^2 +(-1)^2) `
`= sqrt(9+1) = sqrt(10) `
`BC = sqrt((4-6)^2 +(3-6)^2) = sqrt((-2)^2 +(-3)^2)`
`= sqrt(4+9) = sqrt(13)`
`CD = sqrt((6-3) ^2 +(6-5)^2) = sqrt((3)^2 +(1)^2) `
`= sqrt(9+1) = sqrt(10)`
`AD = sqrt((1-3)^2 +(2-5)^2 ) = sqrt((-2)^2 +(-3)^2)`
`= sqrt(4+9) = sqrt(13) `
`∵ AB = CD = sqrt(10) " units and" BC= AD = sqrt(13) units `
Therefore, ABCD is a parallelogram
`AC = sqrt((1-6)^2 +(2-6)^2 )= sqrt((-5)^2 +(-4)^2)`
`= sqrt(25+16) = sqrt(41) `
`BD = sqrt((4-3)^2 +(3-5)^2 ) = sqrt((1)^2 +(-2)^2) `
`= sqrt(1+4) = sqrt(5) `
Thus, the diagonal AC and BD are not equal and hence ABCD is not a rectangle
APPEARS IN
संबंधित प्रश्न
Find the centre of the circle passing through (5, -8), (2, -9) and (2, 1).
Prove that the points (0, 0), (5, 5) and (-5, 5) are the vertices of a right isosceles triangle.
Name the quadrilateral formed, if any, by the following points, and given reasons for your answers:
A(-1,-2) B(1, 0), C (-1, 2), D(-3, 0)
Find the coordinates of the points which divide the line segment joining the points (-4, 0) and (0, 6) in four equal parts.
In what ratio does the point (−4, 6) divide the line segment joining the points A(−6, 10) and B(3,−8)?
Find the ratio in which the point (−3, k) divides the line-segment joining the points (−5, −4) and (−2, 3). Also find the value of k ?
Mark the correct alternative in each of the following:
The point of intersect of the coordinate axes is
what is the value of \[\frac{a^2}{bc} + \frac{b^2}{ca} + \frac{c^2}{ab}\] .
Write the coordinates the reflections of points (3, 5) in X and Y -axes.
Write the formula for the area of the triangle having its vertices at (x1, y1), (x2, y2) and (x3, y3).
Find the distance between the points \[\left( - \frac{8}{5}, 2 \right)\] and \[\left( \frac{2}{5}, 2 \right)\] .
If P (2, 6) is the mid-point of the line segment joining A(6, 5) and B(4, y), find y.
The coordinates of the point on X-axis which are equidistant from the points (−3, 4) and (2, 5) are
If A (5, 3), B (11, −5) and P (12, y) are the vertices of a right triangle right angled at P, then y=
The coordinates of the point P dividing the line segment joining the points A (1, 3) and B(4, 6) in the ratio 2 : 1 are
A line intersects the y-axis and x-axis at P and Q , respectively. If (2,-5) is the mid-point of PQ, then the coordinates of P and Q are, respectively
What is the nature of the line which includes the points (-5, 5), (6, 5), (-3, 5), (0, 5)?
Which of the points P(-1, 1), Q(3, - 4), R(1, -1), S (-2, -3), T(-4, 4) lie in the fourth quadrant?
If segment AB is parallel Y-axis and coordinates of A are (1, 3), then the coordinates of B are ______
Write the X-coordinate and Y-coordinate of point P(– 5, 4)
