Advertisements
Advertisements
Question
Equations of diagonals of the square formed by the lines x = 0, y = 0, x = 1 and y = 1 are ______.
Options
y = x, y + x = 1
y = x, x + y = 2
2y = x, y + x = `1/3`
y = 2x, y + 2x = 1
Advertisements
Solution
Equations of diagonals of the square formed by the lines x = 0, y = 0, x = 1 and y = 1 are y = x, y + x = 1.
Explanation:
Given equation x = 0, y = 0
x = 1 and y = 1 form a square of side 1 unit
From figure, we get that OABC is square having corners O(0, 0), A(1, 0), B(1, 1) and C(0, 1)
Equation of diagonal AC
y – 0 = `(1 - 0)/(0 - 1) (x - 1)`
⇒ y = – (x – 1)
⇒ y = – x + 1
⇒ y + x = 1
Equation of diagonal OB is y – 0 = `(1 - 0)/(1 - 0) (x - 0)`
⇒ y = x
APPEARS IN
RELATED QUESTIONS
Draw a quadrilateral in the Cartesian plane, whose vertices are (–4, 5), (0, 7), (5, –5) and (–4, –2). Also, find its area.
Find the distance between P (x1, y1) and Q (x2, y2) when :
- PQ is parallel to the y-axis,
- PQ is parallel to the x-axis
Without using distance formula, show that points (–2, –1), (4, 0), (3, 3) and (–3, 2) are vertices of a parallelogram.
Consider the given population and year graph. Find the slope of the line AB and using it, find what will be the population in the year 2010?
Find the values of k for which the line (k–3) x – (4 – k2) y + k2 –7k + 6 = 0 is
- Parallel to the x-axis,
- Parallel to the y-axis,
- Passing through the origin.
Find the equation of a line drawn perpendicular to the line `x/4 + y/6 = 1`through the point, where it meets the y-axis.
Find the slope of the lines which make the following angle with the positive direction of x-axis:
\[\frac{2\pi}{3}\]
Find the slope of the lines which make the following angle with the positive direction of x-axis:
\[\frac{3\pi}{4}\]
State whether the two lines in each of the following are parallel, perpendicular or neither.
Through (9, 5) and (−1, 1); through (3, −5) and (8, −3)
State whether the two lines in each of the following is parallel, perpendicular or neither.
Through (6, 3) and (1, 1); through (−2, 5) and (2, −5)
Using the method of slope, show that the following points are collinear A (4, 8), B (5, 12), C (9, 28).
What can be said regarding a line if its slope is zero ?
Without using Pythagoras theorem, show that the points A (0, 4), B (1, 2) and C (3, 3) are the vertices of a right angled triangle.
Find the angle between X-axis and the line joining the points (3, −1) and (4, −2).
Show that the perpendicular bisectors of the sides of a triangle are concurrent.
Find the angles between the following pair of straight lines:
3x + y + 12 = 0 and x + 2y − 1 = 0
Find the angles between the following pair of straight lines:
(m2 − mn) y = (mn + n2) x + n3 and (mn + m2) y = (mn − n2) x + m3.
Show that the tangent of an angle between the lines \[\frac{x}{a} + \frac{y}{b} = 1 \text { and } \frac{x}{a} - \frac{y}{b} = 1\text { is } \frac{2ab}{a^2 - b^2}\].
Write the coordinates of the image of the point (3, 8) in the line x + 3y − 7 = 0.
The reflection of the point (4, −13) about the line 5x + y + 6 = 0 is
If m1 and m2 are slopes of lines represented by 6x2 - 5xy + y2 = 0, then (m1)3 + (m2)3 = ?
Find the equation of the straight line passing through (1, 2) and perpendicular to the line x + y + 7 = 0.
Find the equation to the straight line passing through the point of intersection of the lines 5x – 6y – 1 = 0 and 3x + 2y + 5 = 0 and perpendicular to the line 3x – 5y + 11 = 0.
The coordinates of the foot of the perpendicular from the point (2, 3) on the line x + y – 11 = 0 are ______.
The reflection of the point (4, – 13) about the line 5x + y + 6 = 0 is ______.
Find the equation of the line passing through the point (5, 2) and perpendicular to the line joining the points (2, 3) and (3, – 1).
Show that the tangent of an angle between the lines `x/a + y/b` = 1 and `x/a - y/b` = 1 is `(2ab)/(a^2 - b^2)`
If the equation of the base of an equilateral triangle is x + y = 2 and the vertex is (2, – 1), then find the length of the side of the triangle.
P1, P2 are points on either of the two lines `- sqrt(3) |x|` = 2 at a distance of 5 units from their point of intersection. Find the coordinates of the foot of perpendiculars drawn from P1, P2 on the bisector of the angle between the given lines.
If p is the length of perpendicular from the origin on the line `x/a + y/b` = 1 and a2, p2, b2 are in A.P, then show that a4 + b4 = 0.
The equation of the straight line passing through the point (3, 2) and perpendicular to the line y = x is ______.
The tangent of angle between the lines whose intercepts on the axes are a, – b and b, – a, respectively, is ______.
One vertex of the equilateral triangle with centroid at the origin and one side as x + y – 2 = 0 is ______.
Line joining the points (3, – 4) and (– 2, 6) is perpendicular to the line joining the points (–3, 6) and (9, –18).
The equation of the line through the intersection of the lines 2x – 3y = 0 and 4x – 5y = 2 and
| Column C1 | Column C2 |
| (a) Through the point (2, 1) is | (i) 2x – y = 4 |
| (b) Perpendicular to the line (ii) x + y – 5 = 0 x + 2y + 1 = 0 is |
(ii) x + y – 5 = 0 |
| (c) Parallel to the line (iii) x – y –1 = 0 3x – 4y + 5 = 0 is |
(iii) x – y –1 = 0 |
| (d) Equally inclined to the axes is | (iv) 3x – 4y – 1 = 0 |
The line which passes through the origin and intersect the two lines `(x - 1)/2 = (y + 3)/4 = (z - 5)/3, (x - 4)/2 = (y + 3)/3 = (z - 14)/4`, is ______.
A ray of light coming from the point (1, 2) is reflected at a point A on the x-axis and then passes through the point (5, 3). The co-ordinates of the point A is ______.
