Advertisements
Advertisements
प्रश्न
A(2, 5), B(1, 0), C(−4, 3) and D(–3, 8) are the vertices of quadrilateral ABCD. Find the co-ordinates of the mid-points of AC and BD. Give a special name to the quadrilateral.
उत्तर
Co-ordinates of A = (2, 5), of B = (1, 0), of C = (−4, 3) and of D = (−3, 8)
Let the mid-point of AC is P(x1, y1)
∴ Co-ordinates of mid-point of AC will be
`(x_1, y_1) = ((2 - 4)/2, (5 + 3)/2)`
=`((-2)/2, 8/2)`
= (−1, 4)
Let the mid-point of BD is Q(x2, y2)
Co-ordinates of mid-point of BD will be
∴ `(x_2, y_2) = ((1 + (-3))/2, (0 + 8)/2)`
= `((1 - 3)/2, 8/2)`
= `((-2)/2, 8/2)`
= (−1, 4)
∵ Co-ordinates of mid-points AC and BD are the same.
∴ The quadrilateral is a parallelogram.
APPEARS IN
संबंधित प्रश्न
Calculate the co-ordinates of the centroid of the triangle ABC, if A = (7, –2), B = (0, 1) and C =(–1, 4).
Write the co-ordinates of the point of intersection of graphs of
equations x = 2 and y = -3.
P( -2, 5), Q(3, 6 ), R( -4, 3) and S(-9, 2) are the vertices of a quadrilateral. Find the coordinates of the midpoints of the diagonals PR and QS. Give a special name to the quadrilateral.
Two vertices of a triangle are (1, 4) and (3, 1). If the centroid of the triangle is the origin, find the third vertex.
If P(–b, 9a – 2) divides the line segment joining the points A(–3, 3a + 1) and B(5, 8a) in the ratio 3: 1, find the values of a and b.
If the mid-point (x, y) of the line joining (3, 4) and (p, 7) lies on 2x + 2y + 1 = 0, then what will be the value of p?
The points A(−5, 4), B(−1, −2) and C(5, 2) are the vertices of an isosceles right-angled triangle where the right angle is at B. Find the coordinates of D so that ABCD is a square
A(−3, 2), B(3, 2) and C(−3, −2) are the vertices of the right triangle, right angled at A. Show that the mid-point of the hypotenuse is equidistant from the vertices
If the coordinates of one end of a diameter of a circle is (3, 4) and the coordinates of its centre is (−3, 2), then the coordinate of the other end of the diameter is
Find the co-ordinates of centroid of a triangle if points D(–7, 6), E(8, 5) and F(2, –2) are the mid-points of the sides of that triangle.
