DSQ: Calculating the slope of a perpendicular line - GMAT Quantitative

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

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.

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.

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

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.

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.

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

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.

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.

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

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.

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.

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

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.

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.

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

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.

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.

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