DSQ: Calculating the slope of a perpendicular line - GMAT Quantitative Reasoning
Card 0 of 3
Consider 
and 
.
Find the slope of 
.
I) 
passes through the point 
.
II) 
is perpendicular to 
.
Consider
Find the slope of
I)
II)
We are given a line, f(x), and asked to find the slope of another line, h(x).
I) Gives a point on h(x). We could plug in the point and solve for our slope. When we do this since x=0 we are unable to find the value for our slope. Therefore, statement I is not sufficient to solve the question.
II) Tells us the two lines are perpendicular. Take the opposite reciprocal of the slope of f(x) to find the slope of h(x).
Therefore,
and thus the slope of h(x) will be,
.
Statement II is sufficient to answer the question.
We are given a line, f(x), and asked to find the slope of another line, h(x).
I) Gives a point on h(x). We could plug in the point and solve for our slope. When we do this since x=0 we are unable to find the value for our slope. Therefore, statement I is not sufficient to solve the question.
II) Tells us the two lines are perpendicular. Take the opposite reciprocal of the slope of f(x) to find the slope of h(x).
Therefore,
and thus the slope of h(x) will be,
Statement II is sufficient to answer the question.
Compare your answer with the correct one above
Calculate the slope of a line perpendicular to line 
.
- Line
passes through points 
and 
.
- The equation for line
is 
.
Calculate the slope of a line perpendicular to line
- Line
- The equation for line
Statement 1: We can use the points provided to find the slope of line AB.
Since the slope we're being asked for is of a line perpendicular to line AB, their slopes are inverses of each other.
The slope of our line is then 
Statement 2: Since we're provided with the line's equation, we just need to look for the slope.
Where 
is the slope and 
is the y-intercept.
In this case, we have 
so 
. Because our line is perpendicular to line AB, the slope we're looking for is 
Statement 1: We can use the points provided to find the slope of line AB.
Since the slope we're being asked for is of a line perpendicular to line AB, their slopes are inverses of each other.
The slope of our line is then
Statement 2: Since we're provided with the line's equation, we just need to look for the slope.
Where
In this case, we have
Compare your answer with the correct one above
Find the slope of a line perpendicular to 
.
I) 
passes through the points 
and 
.
II) 
does not pass through the origin.
Find the slope of a line perpendicular to
I)
II)
Find the slope of a line perpendicular to g(t)
I) g(t) passes through the points (9,6) and (4,-13)
II) g(t) does not pass through the origin
Perpendicular lines have opposite reciprocal slopes. For instance: a line with a slope of 
would be perpendicular to a line with slope of 
.
To find the slope of a line, we just need two points.
I) Gives us two points on g(t). We could find the slope of g(t) and then the slope of any line perpendicular to g(t).
So the slope of a line perpendicular to g(t) is equal to:
II) Is irrelevant or at least not helpful.
Find the slope of a line perpendicular to g(t)
I) g(t) passes through the points (9,6) and (4,-13)
II) g(t) does not pass through the origin
Perpendicular lines have opposite reciprocal slopes. For instance: a line with a slope of
To find the slope of a line, we just need two points.
I) Gives us two points on g(t). We could find the slope of g(t) and then the slope of any line perpendicular to g(t).
So the slope of a line perpendicular to g(t) is equal to:
II) Is irrelevant or at least not helpful.
Compare your answer with the correct one above