Analyzing Straight Line Equations
We are given three straight lines:
- Line 1: $x + y - 3 = 0$
- Line 2: $x + y + 2 = 0$
- Line 3: $3x + 3y - 7 = 0$
To determine their relationship, we need to find the slope of each line. The slope ($m$) of a line in the form $Ax + By + C = 0$ is given by $m = -A/B$.
Calculating Slopes
- For Line 1 ($x + y - 3 = 0$): $A=1, B=1$. Slope $m_1 = -1/1 = -1$.
- For Line 2 ($x + y + 2 = 0$): $A=1, B=1$. Slope $m_2 = -1/1 = -1$.
- For Line 3 ($3x + 3y - 7 = 0$): $A=3, B=3$. Slope $m_3 = -3/3 = -1$.
Determining Line Relationship
We observe that the slopes of all three lines are equal ($m_1 = m_2 = m_3 = -1$).
Lines with equal slopes are either parallel or the same line.
To check if they are the same line, we compare their constant terms (C):
- Line 1: $C_1 = -3$
- Line 2: $C_2 = 2$
- Line 3: $C_3 = -7$
Since the constant terms are different, the lines are distinct.
Three distinct lines with the same slope are parallel to each other.
Similar Questions
- Find the relation between x and y such that the point (x, y) is equidistant from (6, 2) and (4, 6).
- Find the area of a triangle formed by $(1, 0)$, $(-1, 0)$, $(0, 1)$.
- The points A (1, 2), B (3, 4) and C (4, 1) are the vertices of a triangle which is:
- The image of the point $(7, 8)$ when reflected along the x-axis is:
- The equation of a straight line passing through (-2,5) and (1,3) is:
- The intercepts made by the plane $3x - 4y - 2z = 6$ with the coordinate axis are:
- Find the relation between x and y such that the point (x, y) is equidistant from (5, 3) and (4, 6).
- The distance between two points $(a \cos \alpha, 0)$ and $(0, a \sin \alpha)$ is_____.
- The area of the triangle formed by the line $2x - 4y - 7 = 0$ with the coordinate axis is:
- The distance from the origin to the line $4x + 3y + 6 = 0$ is:
Important Questions from Coordinate Geometry
What is the reflection of the point (-1, 5) in the line x = 1?
What are the co-ordinates of the centroid of a triangle, whose vertices are A(1, -5), B(-4, 0) and C(3, -4)?
Slope of the line AB is 4/3. Co-ordinates of points A and B are (x, -5) and (2, -3) respectively. What is the value of x?
Find the co-ordinates of the centroid of a triangle whose vertices are A(1, 4), B(7, 8) and C(10, 12).
- If x² + y² - 12x + 18y + 117 = 0, then the value of x² + y² is:
