If P0 = (x0, y0) is the point on the line 2x y = 1 closest to the origin, what is the value of x0?

The affiliate ten Straight Lines will be your dose for mathematical geometry as per class xi maths syllabus. Every bit geometry has been an integral part of the curriculum since inferior classes, the same is even followed in class 11th and 12th. You must take been through the graphical representation of equations via chapters like linear equation in one variable. Thus, class 11 directly lines affiliate will equip you lot with advanced cognition of this concept. And then let'south get through our notes and understand the chapter.

This Web log Includes:

1. What is a Straight Line?
2. Slope of a Line
3. Various Forms of the Equation of a Line
   1. Horizontal and Vertical Lines
4. General Equation of a Line
   1. Slope-Intercept Course
   2. Intercept Form
5. Altitude between Two Parallel Lines
6. Directly Lines: Practice Questions

What is a Straight Line?

Any line that can be traced by a bespeak travelling in a management with nada curvature is known as a straight line. A straight line extends in two directions forever while having but one dimension and length. Information technology is an important concept of geometry that is useful in various ways.

Slope of a Line

To stand for a line algebraically, the slope is an essential office because, in a coordinate airplane, it forms two angles with the 10-axis in supplementary course. As per class 11 straight lines chapter, the slope of a line can be determined with the value of tan θ. Wherein, within the positive management of the line in an anti-clock direction, an angle is made by θ.

If the slope of the line passes through two points, i.due east., P (a1, b1) and Q (a1, b2), then it becomes: thou = tan θ = b2-b1/a2-a1.

Let u.s. empathize this through an instance, let P (a1, b1) and Q (a1, b2) be any two points on a non-vertical line. The inclination of these lines will exist θ, and it volition be acute or birdbrained. Nether both the scenarios, the slope of the line will pass through signal P and Q merely.

Take This Maths Quiz If You Consider Yourself Genius!

Various Forms of the Equation of a Line

Form 11 maths NCERT states that every line in a aeroplane has infinitely many points. By using the relationship between the line and points, several equations can be solved. Beneath mentioned are different conditions that explain the equations of a line.

Horizontal and Vertical Lines

Derived form class 11 direct lines under this condition, if a horizontal line is distanced from a betoken to the x-axis, then every point will ordinate either positive or negative respectively, i.e., +a or -a. Similarly, it will be aforementioned for the vertical line also, but from a dissimilar axis than x-axis, i.e., y-axis.

Signal-Gradient Grade
Allow P0 (x0, y0) be a fixed point on a not-vertical line with assumed gradient "k". If P (10, y) is an arbitrary betoken on the non-vertical line and so, the bespeak (x, y) will lie with slope "thousand" on the same line through the fixed betoken (x0, y0) with equation y – y0 = g (x – x0).

Two-Point Form
If an imaginary line "L" passes through whatever two given points, i.due east. P1 (x1, y1) and P2 (x2, y2) then, with general point P (x, y), all the three points, i.e. P1, P2, and P3 volition be collinear, and the equation volition be y−y1 = y2−y1 / x2−x1 * (x−x1).

Gradient-Intercept Form
Let us assume that a line cuts the slope from the y-axis at a distance "c", then the altitude "c" volition be called a y-intercept of the line. When the line meets the y-axis, the coordinates will exist (0, c) and the equation will exist y = mx + c wherein the "c" can be positive or negative every bit mentioned in class 11 straight lines. If the line makes an x-intercept of the line instead of the y-intercept of the line, and then the equation will exist y = m (10-d).

Intercept-Form
If a line makes "x-intercept a" and "y-intercept b" on any axis and the line meets x-centrality at signal (a, 0) and y-centrality at betoken (0, b), then the equation co-ordinate to two forms will exist 10/a + y/b = 1.Go through the class 11 maths NCERT solutions and go a good grip over the topic.

Full general Equation of a Line

A full general equation of first degree in two variables volition always exist Ax + Past + C = 0. Wherein A, B, and C will be existent constants with A and B a non-nil value. Graph of such an equation will always be a straight line, and therefore the equation Ax + By + C = 0 is called a general linear equation or general equation of a line. Co-ordinate to class 11 directly lines chapter, the general equation can be reduced into several other forms of equations by using the slope-intercept course, intercept form, and normal form.

Gradient-Intercept Form

If B is non equals to 0, then the equation Ax + By + C = 0 can be rewritten as y = mx + c. If B equals to zero, and so x = -c/a.

Intercept Form

If C is not equals to 0, then the equation Ax + By + C = 0 can be rewritten equally ten/a + y/b = ane. If C equals to 0, and so the equation Ax + By + C = 0 tin be rewritten as Ax + By = 0.

Distance betwixt Two Parallel Lines

The slopes of two parallel lines will always be equal is one of the most essential concepts that are mentioned in class xi straight lines chapter. If nosotros take two parallel lines in the form of y = mx + c1 and y = mc + c2, then the altitude between the two lines volition exist equal to the length of the perpendicular. The equation for the two lines can be written as Ax + By + C1 = 0 and Ax + By + C2 = 0.

Let u.s. have a look at solved example-

Q: If points (10, i), (2, ane), and (four, 5) are collinear, and then notice the value of 10.

Solution: The slope of AB = Slope of BC
(1+i) / (ii-x) = (5-i) / (4-2)
2 / (two-10) = two
2 = two * (2-x)
2 = four – 2x
2x = 2
ten = 2 / 2
x = 1

Directly Lines: Practice Questions

Here are some practices questions based on the like concepts every bit mentioned in form eleven straight lines chapter.

1. In the given equation 2x + y – 3 =0, 5x + ky – 3 = 0 and 3x – y – ii = 0, if all the iii lines are concurrent, and then find the value of 1000.
2. If a line is passing through the betoken (ii, iii) with an angle of 60° from the x-axis, and so discover the equation of the line.
3. What will be the altitude of a point from a line?
4. Observe the altitude betwixt parallel lines 15x + 8y – 34 = 0 and 15x + 8y + 31 = 0.
5. How coordinated geometry and analytical geometry are related to each other?
6. Find the measure out of the angle in between the lines x+y+7=0 and 10-y+ane=0.
7. Find the equation of the line, which makes intercepts -3 and 2 on the x and y-axis respectively.
8. Find the points on the x-axis whose distance from the line equation (x/three) + (y/four) = 1 is given every bit 4units.
9. At what bespeak is the origin shifted, if the coordinates of the point (,5)become (3,7)?
10.  Find the intercepts cut off by the line 2a-b+16=0
11.  Observe the slope of the line, which makes an bending of 30° with the positive direction of y-axis measured anticlockwise.
12.  Determine x so that the inclination of the line containing the points (10,-iii) and (2,5) is 135.
13.  Find the equation of the line which passes through the betoken (3,4) and the sum of whose intercepts on the axes is 14.
14.  Using slopes, find the value of x for which the points (x,-1) (2,1) and (iv,5) are collinear.
15.  Find the value of K, given that the distance of the point (4,1) from the line 3x-4y+k=0 IS four units.

Thus, we promise that through this blog that aims to explain the cadre fundamentals of class eleven straight lines with informative examples, you have understood the chapter in an easy to understand way. If you are clueless about how to proceed in the correct direction leading towards your career goals, reach out to our career experts at Leverage Edu and they will guide yous the best. Book an east-meeting now!

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