Advertisements
Advertisements
Question
Solution
We have to prove that ABCD is a rhombus
Slope of AC = `("y"_2 - "y"_1)/("x"_2 - "x"_1) = (5 - 8)/(0 - 5) = (-3)/(-5) = 3/5`
Slope of BD = `("y"_2 - "y"_1)/("x"_2 - "x"_1) = (9- 4)/(1 - 4) = 5/(-3)`
Thus,Slope of AC x slope of BD = -1
So, the diagnols AC and BC are perpendicular to each other.
Hence,ABCD is a rhombus.
APPEARS IN
RELATED QUESTIONS
The slope of a line joining P(6, k) and Q(1 – 3k, 3) is `1/2`. Find:
- k.
- mid-point of PQ, using the value of ‘k’ found in (i).
Find the value(s) of k so that PQ will be parallel to RS. Given : P(5, −1), Q(6, 11), R(6, −4k) and S(7, k2)
The lines represented by 4x + 3y = 9 and px – 6y + 3 = 0 are parallel. Find the value of p.
If the lines y = 3x + 7 and 2y + px = 3 are perpendicular to each other, find the value of p.
The ordinate of a point lying on the line joining the points (6, 4) and (7, –5) is –23. Find the coordinates of that point.
Find the slope of the lines passing through the given point.
A(2, 3), B(4, 7)
Find the slope of the lines passing through the given point.
L (–2, –3) , M (–6, –8)
Fill in the blank using correct alternative.
Out of the following, point ........ lies to the right of the origin on X– axis.
Find the slope of a line, correct of two decimals, whose inclination is 45°
If A(6, 1), B(8, 2), C(9, 4) and D(7, 3) are the vertices of `square`ABCD, show that `square`ABCD is a parallelogram.
Solution:
Slope of line = `("y"_2 - "y"_1)/("x"_2 - "x"_1)`
∴ Slope of line AB = `(2 - 1)/(8 - 6) = square` .......(i)
∴ Slope of line BC = `(4 - 2)/(9 - 8) = square` .....(ii)
∴ Slope of line CD = `(3 - 4)/(7 - 9) = square` .....(iii)
∴ Slope of line DA = `(3 - 1)/(7 - 6) = square` .....(iv)
∴ Slope of line AB = `square` ......[From (i) and (iii)]
∴ line AB || line CD
∴ Slope of line BC = `square` ......[From (ii) and (iv)]
∴ line BC || line DA
Both the pairs of opposite sides of the quadrilateral are parallel.
∴ `square`ABCD is a parallelogram.
