Advertisements
Advertisements
प्रश्न
Show that the line joining (2, – 3) and (- 5, 1) is:
(i) Parallel to line joining (7, -1) and (0, 3).
(ii) Perpendicular to the line joining (4, 5) and (0, -2).
उत्तर
Let m1 be the slope of line joining (2, -3) and (-5, 1) then
m1 = `(Y-2 - y_1)/(x_2 - x_1)`
= `(1 - (-3))/(-5 - 2) = -(4)/(7)`
(i) Let m2 be the slope of the line joining (7, -1) and (0, 3), then
m2 = `(3 - (-1))/(0, 7) = -(4)/(7)`
Since, m1 = m2, the two lines are parallel.
Hence proved.
(ii) Let m3 be the slope of the line joining (4, 5) and (0, -2) then
m3 = `(-2 - 5)/(0 - 4) = (7)/(4)`
Now m1m3 = `-(4)/(7) xx (7)/(4)` = -1
Hence, the two lines are perpendicular.
Hence proved.
APPEARS IN
संबंधित प्रश्न
Find the slope of the line which is parallel to `x/2 - y/3 -1 = 0 `
Find the value of k for which the lines kx – 5y + 4 = 0 and 5x – 2y + 5 = 0 are perpendicular to each other.
Determine whether the following point is collinear.
A(–4, 4), \[K\left( - 2, \frac{5}{2} \right),\] N (4, –2)
Fill in the blank using correct alternative.
Distance of point (–3, 4) from the origin is ______.
Show that points P(1, –2), Q(5, 2), R(3, –1), S(–1, –5) are the vertices of a parallelogram.
Find the slope and the y-intercept of the following line 2x + 3y = 12
Find the slope and the y-intercept of the following line x - 2 = `(5 - 3"y")/2`
Verify whether the following points are collinear or not:
A(1, –3), B(2, –5), C(–4, 7).
A line passing through the points (a, 2a) and (- 2, 3) is perpendicular to the line 4a + 3y + 5 = 0. Find the value of a.
The line through P (5, 3) intersects Y axis at Q.
(i) Write the slope of the line.
(ii) Write the equation of the line.
(iii) Find the coordinates of Q.
