Coordinate Plane - ACT Math

First, we must solve the equation for y to determine the slope: y = 2_x_ + 3/2

By looking at the coefficient in front of x, we know that the slope of this line has a value of 2. To fine the slope of any line perpendicular to this one, we take the negative reciprocal of it:

slope = m , perpendicular slope = – 1/m

slope = 2 , perpendicular slope = – 1/2

Find the slope of the given line. The perpendicular slope will be the opposite reciprocal of the original slope. Use the slope-intercept form (y = mx + b) and substitute in the given point and the new slope to find the intercept, b. Convert back to standard form of an equation: ax + by = c.

First rearrange the equation so that it is in slope-intercept form, resulting in y=2/3 x + 14/9. The slope of this line is 2/3, so the slope of the line perpendicular will have the opposite reciprocal as a slope, which is -3/2.

Perpendicular lines have slopes that are the opposite of the reciprocal of each other. In this case, the slope of the first line is -2. The reciprocal of -2 is -1/2, so the opposite of the reciprocal is therefore 1/2.

The question puts the line in point-slope form y – y1 = m(x – x1), where m is the slope. Therefore, the slope of the original line is 1/2. A line perpendicular to another has a slope that is the negative reciprocal of the slope of the other line. The negative reciprocal of the original line is _–_2, and is thus the slope of its perpendicular line.

The equation of a line is where is the slope.

Rearrange the equation to match this:

For the perpendicular line, the slope is the negative reciprocal;

therefore

First we must find the slope of the given line. The slope of y = –3x – 4 is –3. The slope of the perpendicular line is the negative reciprocal. This means you change the sign of the slope to its opposite: in this case to 3. Then find the reciprocal by switching the denominator and numerator to get 1/3; therefore the slope of the perpendicular line is 1/3.

First, you must find the slope of the line given to you. Remember that the slope is calculated:

Thus, for our data, this is:

Now, the perpendicular slope to this is opposite and reciprocal. Hence, it must be . This only holds for the equation

To know this, solve the equation for the format . This will let you find the slope very quickly, for it is . First, add to both sides:

Next, divide everything by :

You really just need to pay attention to the term. This reduces to , which is just what you need!

Perependicular lines have slopes whose product is .

and so the answer is

To find the slope of a perpendicular line, we take the reciprocal of the known slope , where .

The easy way to do this is to simply take the fraction (a whole slope can be made into a fraction by placing in the denominator), exchange the numerator and denominator, then multiply the fraction by Thus,

.

To find the slope of a perpendicular line, we take the reciprocal of the known slope , where .

The easy way to do this is to simply take the fraction (a whole slope can be made into a fraction by placing in the denominator), exchange the numerator and denominator, then multiply the fraction by

However, if we attempt to follow this procedure, we get:

, which is undefined.

Thus, our perpendicular line (which is a vertical line) has an undefined slope.

Perpendicular lines will have slopes that are negative reciprocals of one another. Our first step will be to find the slope of the given line by putting the equation into slope-intercept form.

The slope of this line is .

First let's find the negative of the current slope.

Now, we need to find the reciprocal of . In order to find the reciprocal of a number we divide one by that number; therefore, we can calculate the following:

The negative reciprocal will be or which will be the slope of the perpendicular line.

The midpoint of a line segment is found using the formula .

The midpoint is given as Going through the answer choices, only the points and yield the correct midpoint of .

To get from the midpoint of (12, **–**3) to point (3,4), we travel **–**9 units in the x-direction and 7 units in the y-direction. To find the other point, we travel the same magnitude in the opposite direction from the midpoint, 9 units in the x-direction and **–**7 units in the y-direction to point (21, **–**10).

The midpoint formula can be used to solve this problem, where the midpoint is the average of the two coordinates.

We are given the midpoint and one endpoint. Plug these values into the formula.

Solve for the variables to find the coordinates of the second endpoint.

The final coordinates of the other endpoint are .

What is the midpoint of the segment of

between and ?

To find this midpoint, you must first calculate the two end points. Thus, substitute in for :

Then, for :

Thus, the two points in question are:

and

The midpoint of two points is:

Thus, for our data, this is:

or

If is the midpoint of and another point, what is that other point?

Recall that the midpoint's and values are the average of the and values of the two points in question. Thus, if we call the other point , we know that:

and

Solve each equation accordingly:

For , multiply both sides by and then subtract from both sides:

Thus,

For , multiply both sides by 2 and then subtract 10 from both sides:

Thus,

Thus, our point is

Recall that the midpoint's and values are the average of the and values of the two points in question. Thus, if we call the other point , we know that:

and

Solve each equation accordingly:

For , multiply both sides by :

Thus,

The same goes for the other equation:

, so

Thus, our point is

First, put the equation in slope-intercept form: y = 3x + 6. From there we can see the slope of this line is 3 and since the slope of any line parallel to another line is the same, the slope will also be 3.

We rearrange the line to express it in slope intercept form.

Any line parallel to this original line will have the same slope.