# GMAT Math : DSQ: Calculating the slope of a perpendicular line

## Example Questions

### Example Question #1 : Lines

Calculate the slope of a line perpendicular to line .

1. Line  passes through points  and .
2. The equation for line  is .

Statements 1 and 2 are not sufficient, and additional data is needed to answer the question.

Statement 1 alone is sufficient, but statement 2 alone is not sufficient to answer the question.

Statement 2 alone is sufficient, but statement 1 alone is not sufficient to answer the question.

Each statement alone is sufficient to answer the question.

Both statements taken together are sufficient to answer the question, but neither statement alone is sufficient.

Each statement alone is sufficient to answer the question.

Explanation:

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

### Example Question #2 : Dsq: Calculating The Slope Of A Perpendicular Line

Find the slope of a line perpendicular to .

I)  passes through the points  and .

II)  does not pass through the origin.

Either statement is sufficient to answer the question.

Statement I is sufficient to answer the question, but statement II is not sufficient to answer the question.

Statement II is sufficient to answer the question, but statement I is not sufficient to answer the question.

Neither statement is sufficient to answer the question. More information is needed.

Both statements are needed to answer the question.

Statement I is sufficient to answer the question, but statement II is not sufficient to answer the question.

Explanation:

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.

### Example Question #3 : Dsq: Calculating The Slope Of A Perpendicular Line

Consider  and .

Find the slope of .

I)  passes through the point .

II)  is perpendicular to .

Neither statement is sufficient to answer the question. More information is needed.

Statement II is sufficient to answer the question, but Statement I is not sufficient to answer the question.

Statement I is sufficient to answer the question, but Statement II is not sufficient to answer the question.

Either statement alone is sufficient to answer the question.

Both statements together are needed to answer the question.

Statement II is sufficient to answer the question, but Statement I is not sufficient to answer the question.

Explanation:

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.

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