Maths-
General
Easy
Question
Identify the equation of a line perpendicular to the line x/2 + y = -1
- y = -
x - y = - x
- y - 2x = 0
- y + 2x = 0
xThe correct answer is: y - 2x = 0
Hint:-
1. The slope of a line can be defined as the change in y coordinates of any 2 points on that line corresponding to the change in the x coordinates of those 2 points. This is generally referred to as the rise to run ratio of the given line i.e. how much did the y-coordinates rise vis-a-vis how long a distance was covered by the x-coordinates. Slope = m = rise / run = y2-y1 / x2-x1
2. Slopes of perpendicular lines are negative reciprocals of each other.
Step-by-step solution:-
x/2 + y = -1
∴ y = -1 - x/2
i.e. Y = -1/2 x - 1
Comparing the above equation with standard form of a line i.e. y = mx + c, we get-
m = - …...................................................................... (Equation i)
Now, we know that slopes of perpendicular lines are negative reciprocals of each other.
∴ Slope of line perpendicular to the given line = - 1/ slope of given line
∴ Slope of line perpendicular to the given line = - 1/ -
∴ Slope of line perpendicular to the given line = 2
∴ We need to find the line from the given options, whose slope = 2.
a. y = - x
∴ y = - x + 0
Comparing the above equation with standard form of a line i.e. y = mx + c, we get-
m = - ≠ 2
b. y = -x
∴ y = - x + 0
Comparing the above equation with standard form of a line i.e. y = mx + c, we get-
m = - 1 ≠ 2
c. y - 2x = 0
∴ y = 2x + 0
Comparing the above equation with standard form of a line i.e. y = mx + c, we get-
m = 2
d. y + 2x = 0
∴ y = - 2x + 0
Comparing the above equation with standard form of a line i.e. y = mx + c, we get-
m = - 2 ≠ 2
Final Answer:-
∴ Option c i.e. y - 2x = 0 is the correct option.
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