Advertisements
Advertisements
प्रश्न
Show that the given points form a parallelogram:
A(2.5, 3.5), B(10, – 4), C(2.5, – 2.5) and D(– 5, 5)
Advertisements
उत्तर
Let A(2.5, 3.5), B(10, – 4), C(2.5, – 2.5) and D(– 5, 5) are the vertices of a parallelogram.
Slope of a line = `(y_2 - y_1)/(x_2 - x_1)`
Slope of AB = `(-4 - 3.5)/(10 - 2.5) = (-7.5)/(7.5)` = – 1
Slope of CD = `(5 + 2.5)/(-5 - 2.5) = (7.5)/(-7.5)` = – 1
Slope of AB = Slope of CD = – 1
∴ AB is Parallel to CD ...(1)
Slope of BC = `(-4 + 2.5)/(10 - 2.5) = (-1.5)/(7.5) = (-15)/75 = -1/5`
Slope of AD = `(5 - 3.5)/(-5 - 2.5) = 1.5/-7.5 = 15/(-75) = -1/5`
Slope of BC = Slope of AD
∴ BC is parallel to AD
From (1) and (2) we get ABCD is a parallelogram.
APPEARS IN
संबंधित प्रश्न
What is the slope of a line whose inclination with positive direction of x-axis is 0°
What is the inclination of a line whose slope is 0
Show that the given points are collinear: (– 3, – 4), (7, 2) and (12, 5)
The line through the points (– 2, a) and (9, 3) has slope `-1/2` Find the value of a.
The line through the points (– 2, 6) and (4, 8) is perpendicular to the line through the points (8, 12) and (x, 24). Find the value of x.
Let A(3, – 4), B(9, – 4), C(5, – 7) and D(7, – 7). Show that ABCD is a trapezium.
A quadrilateral has vertices at A(– 4, – 2), B(5, – 1), C(6, 5) and D(– 7, 6). Show that the mid-points of its sides form a parallelogram.
The slope of the line which is perpendicular to a line joining the points (0, 0) and (− 8, 8) is
Without using distance formula, show that the points (−2, −1), (4, 0), (3, 3) and (−3, 2) are vertices of a parallelogram
Find the equation of a line passing through the point of intersection of the lines 4x + 7y – 3 = 0 and 2x – 3y + 1 = 0 that has equal intercepts on the axes.
