Coordinate Geometry

Help Questions

GED Math › Coordinate Geometry

Questions 1 - 10

Which of the following equations depicts a line that is perpendicular to the line

$\small y=-\frac{1}{2}x+7$ ?

$\small y=2x+4$

$\small y=-2x-2$

$\small y=\frac{1}{2}x+7$

$\small y=-\frac{1}{2}x+3$

Explanation

The given equation is written in slope-intercept form, and the slope of the line is . The slope of a perpendicular line is the negative reciprocal of the given line. The negative reciprocal here is . Therefore, the correct equation is:

$\small y=2x+4$

Which of the following equations depicts a line that is perpendicular to the line

$\small y=-\frac{1}{2}x+7$ ?

$\small y=2x+4$

$\small y=-2x-2$

$\small y=\frac{1}{2}x+7$

$\small y=-\frac{1}{2}x+3$

Explanation

$\small y=2x+4$

What is the y-intercept of the following equation?

$\frac{5}{2}$

$\frac{2}{5}$

$\frac{5}{3}$

$\frac{3}{2}$

Explanation

The y-intercept is the value of when .

Substitute into the equation.

Divide by 2 on both sides.

$\frac{2y}{2}=\frac{5}{2}$

The answer is: $\frac{5}{2}$

Line

Refer to the above red line. A line is drawn perpendicular to that line, and with the same -intercept. What is the equation of that line in slope-intercept form?

$y = -\frac{1}{2}x-2$

$y = -\frac{1}{2}x-4$

$y = \frac{1}{2}x+4$

$y = \frac{1}{2}x+2$

Explanation

First, we need to find the slope of the above line.

The slope of a line. given two points $(x_{1}, y_{1}), (x_{2}, y_{2})$ can be calculated using the slope formula:

$m = \frac{y_{2}-y_{1}}{x_{2}-x _{1}}$

Set $x_{1}=-4, y_{1}=x_{2}= 0, y_{2}=8$ :

$m = \frac{8-0}{0-(-4)} = \frac{8}{4} = 2$

The slope of a line perpendicular to it has as its slope the opposite of the reciprocal of 2, which would be $m = -\frac{1}{2}$ .

Since we want the line to have the same -intercept as the above line, which is the point , we can use the slope-intercept form to help us. We set

$m = -\frac{1}{2},x= -4, y=0$ , and solve for :

$0 = -\frac{1}{2}(-4)+b$

Substitute for and in the slope-intercept form, and the equation is

$y = -\frac{1}{2}x-2$ .

Line

Refer to the above red line. A line is drawn perpendicular to that line, and with the same -intercept. What is the equation of that line in slope-intercept form?

$y = -\frac{1}{2}x-2$

$y = -\frac{1}{2}x-4$

$y = \frac{1}{2}x+4$

$y = \frac{1}{2}x+2$

Explanation

First, we need to find the slope of the above line.

The slope of a line. given two points $(x_{1}, y_{1}), (x_{2}, y_{2})$ can be calculated using the slope formula:

$m = \frac{y_{2}-y_{1}}{x_{2}-x _{1}}$

Set $x_{1}=-4, y_{1}=x_{2}= 0, y_{2}=8$ :

$m = \frac{8-0}{0-(-4)} = \frac{8}{4} = 2$

The slope of a line perpendicular to it has as its slope the opposite of the reciprocal of 2, which would be $m = -\frac{1}{2}$ .

Since we want the line to have the same -intercept as the above line, which is the point , we can use the slope-intercept form to help us. We set

$m = -\frac{1}{2},x= -4, y=0$ , and solve for :

$0 = -\frac{1}{2}(-4)+b$

Substitute for and in the slope-intercept form, and the equation is

$y = -\frac{1}{2}x-2$ .

What is the y-intercept of the following equation?

$\frac{5}{2}$

$\frac{2}{5}$

$\frac{5}{3}$

$\frac{3}{2}$

Explanation

The y-intercept is the value of when .

Substitute into the equation.

Divide by 2 on both sides.

$\frac{2y}{2}=\frac{5}{2}$

The answer is: $\frac{5}{2}$

Find the and -intercepts for the following equation:

$y = x^{2} - 9$

Explanation

To find the , set equal to 0:

$0 = x^{2} - 9$

Then solve:

$9 = x^{2}$

$\sqrt{9} = \sqrt{x^{2}}$

Remember, the square root of is both and

To find the, set equal to 0:

$y = 0^{2} - 9$

Then solve:

Which of the following lines is perpendicular to the line ?

$y=\frac{4}{3}x-2$

$y=-\frac{4}{3}x-5$

$y=-\frac{1}{4}x-3$

Explanation

Recall that perpendicular lines have slopes that are negative reciprocals.

Start by putting into slope-intercept form.

$y=-\frac{3}{4}x+\frac{5}{8}$

The slope of the given line is $-\frac{3}{4}$ , which means that the line perpendicular to it must have a slope of $\frac{4}{3}$ .

$y=\frac{4}{3}x-2$ is the only line that has the required slope.

Provide your answer in its most simplified form.

Find the distance between the two following points:

$\sqrt{137}$

$\sqrt{55}$

$\sqrt{25}$

Explanation

We must use the distance formula to solve this problem:

$d = \sqrt{(x_{1} - x_{2})^{2} + (y_{1} - y_{2})^{2}}$

Plug in your x and y values:

$d = \sqrt{(2 - 5)^{2} + (2 - 6)^{2}}$

Combine like terms:

$d = \sqrt{(-3)^{2} + (-4)^{2}}$

Continue with your order of operations

$d = \sqrt{9 + 16}$

$d = \sqrt{25}$

Simplify to get:

Find the and -intercepts for the following equation:

$y = x^{2} - 9$

Explanation

To find the , set equal to 0:

$0 = x^{2} - 9$

Then solve:

$9 = x^{2}$

$\sqrt{9} = \sqrt{x^{2}}$

Remember, the square root of is both and

To find the, set equal to 0:

$y = 0^{2} - 9$

Then solve:

Page 1 of 29

Return to subject