Advertisements
Advertisements
प्रश्न
Without using the distance formula, show that the points A(4, 5), B(1, 2), C(4, 3) and D(7, 6) are the vertices of a parallelogram.
उत्तर
The given points are A(4, 5), B(1, 2), C(4, 3) and D(7, 6).
Slope of AB = `(2 - 5)/(1 - 4)`
Slope of AB = `(-3)/(-3)`
Slope of AB = 1
Slope of CD = `(6 - 3)/(7 - 4)`
Slope of CD = `3/3`
Slope of CD = 1
Since, slope of AB = slope of CD
Therefore, AB || CD
Slope of BC = `(3 - 2)/(4 - 1) = 1/3`
Slope of DA = `(5 - 6)/(4 - 7) = (-1)/(-3) = 1/3`
Since, slope of BC = slope of DA
Therefore, BC || DA
Hence, ABCD is a parallelogram
APPEARS IN
संबंधित प्रश्न
(−2, 4), (4, 8), (10, 7) and (11, –5) are the vertices of a quadrilateral. Show that the quadrilateral, obtained on joining the mid-points of its sides, is a parallelogram.
The side AB of an equilateral triangle ABC is parallel to the x-axis. Find the slopes of all its sides.
A(5, 4), B(−3, −2) and C(1, −8) are the vertices of a triangle ABC. Find:
- the slope of the altitude of AB,
- the slope of the median AD and
- the slope of the line parallel to AC.
Find the value(s) of k so that PQ will be parallel to RS. Given : P(3, −1), Q(7, 11), R(−1, −1) and S(1, k)
Determine whether the following point is collinear.
P(2, –5), Q(1, –3), R(–2, 3)
Show that A(–4, –7), B (–1, 2), C (8, 5) and D (5, –4) are the vertices of a parallelogram.
Find the slope of a line passing through the point A (-2,1), B (0,3).
Find the image of a point (-1, 2) in the line joining (2, 1) and (- 3, 2).
If the lines 7y = ax + 4 and 2y = 3 − x, are parallel to each other, then the value of ‘a’ is:
