Advertisements
Advertisements
Question
Without using distance formula, show that the points (−2, −1), (4, 0), (3, 3) and (−3, 2) are vertices of a parallelogram
Solution
The vertices A(−2, −1), B(4, 0), C(3, 3) and D(−3, 2)
Slope of a line = `(y_2 - y_1)/(x_2 - x_1)`
Slope of AB = `(0 + 1)/(4 + 2) = 1/6`
Slope of BC = `(3 - 0)/(3 - 4) = 3/(-1)` = −3
Slope of CD = `(2 - 3)/(-3 - 3) = (-1)/(-6) = 1/6`
Slope of AD = `(2 + 1)/(-3 + 2) = 3/(-1)` = −3
Slope of AB = Slope of CD = `1/6`
∴ AB || CD ...(1)
Slope of BC = Slope of AD = −3
∴ BC || AD ...(2)
From (1) and (2) we get ABCD is a parallelogram.
APPEARS IN
RELATED QUESTIONS
What is the slope of a line whose inclination with positive direction of x-axis is 90°
What is the inclination of a line whose slope is 0
Find the slope of a line joining the points
`(5, sqrt(5))` with the origin
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.
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)
If the points A(2, 2), B(– 2, – 3), C(1, – 3) and D(x, y) form a parallelogram then find the value of x and y.
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
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.
