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GED Math : Geometry and Graphs

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Example Questions

Example Question #851 : Geometry And Graphs

What is the distance between the two points (-10,15) and (-11,-20) ?

Possible Answers:

$\sqrt{1226}$

$19\sqrt{13}$

$55\sqrt{19}$

$15\sqrt{22}$

$\sqrt{2283}$

Correct answer:

$\sqrt{1226}$

Explanation:

Remember that you can consider your two points as:

(x_1,y_1) and (x_2,y_2)

From this, remember that the distance formula is:

$\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$

Now, for your data, this will look like the following. Be very careful with the negative signs:

$\sqrt{(-11-(-10))^2+(-20-15)^2}$

$\sqrt{(-1)^2+(-35)^2}=\sqrt{1+1225}=\sqrt{1226}$

1226 is only factorable into and 613 ; therefore, your answer is in its final form already.

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Example Question #1 : Graphing Lines

A line has slope $\frac{3}{4}$ and -intercept (0, -7) . Give its -intercept.

Possible Answers:

$\left (-5\frac{1}{4}, 0 \right )$

$\left ( 9 \frac{1}{3}, 0 \right )$

$\left (- 9 \frac{1}{3}, 0 \right )$

$\left (5\frac{1}{4}, 0 \right )$

Correct answer:

$\left ( 9 \frac{1}{3}, 0 \right )$

Explanation:

The -intercept will be a point (a,0) for some value . We use the slope formula

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

setting $m = \frac{3}{4}, x_{1} =0, x_{2} = a, y_{1} = -7, y_{2} =0$ ,

and solving for :

$\frac{0- (-7)}{a-0} = \frac{3}{4}$

$\frac{ 7}{a} = \frac{3}{4}$

$\frac{ 7}{a} \cdot a = \frac{3}{4} \cdot a$

$7= \frac{3}{4} \cdot a$

$\frac{4} {3}\cdot 7= \frac{4} {3}\cdot \frac{3}{4} \cdot a$

$a = \frac{28} {3} = 9 \frac{1}{3}$

The -intercept is $\left ( 9 \frac{1}{3}, 0 \right )$ .

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Example Question #851 : Geometry And Graphs

A line has slope $\frac{3}{4}$ and -intercept (5, 0) . Give its -intercept.

Possible Answers:

$\left (0, 3 \frac{3}{4} \right )$

$\left (0, -3 \frac{3}{4} \right )$

$\left (0, -6 \frac{2} {3}\right )$

$\left (0, 6 \frac{2} {3}\right )$

Correct answer:

$\left (0, -3 \frac{3}{4} \right )$

Explanation:

The -intercept will be the point (0, b) for some value . We use the slope formula

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

setting $m = \frac{3}{4}, x_{1} = 5, x_{2} = 0, y_{1} = 0, y_{2} = b$ ,

and solving for :

$\frac{b-0}{0- 5} = \frac{3}{4}$

$\frac{b }{ - 5} = \frac{3}{4}$

$\frac{b }{ - 5} \cdot (-5) = \frac{3}{4} \cdot (-5)$

$b= \frac{-15}{4} = -3 \frac{3}{4}$

The -intercept is $\left (0, -3 \frac{3}{4} \right )$ .

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Example Question #851 : Geometry And Graphs

Axes 1

Above is the graph of the equation $y = - \frac{2}{5}x - 3$ .

Which of the following is the graph of the inequality $y \le - \frac{2}{5}x - 3$ ?

Possible Answers:

Axes 1

Correct answer:

Axes 1

Explanation:

The inequality symbol of the statement

$y \le - \frac{2}{5}x - 3$

allows for the two quantities to be equal, so the line of the equation

$y = - \frac{2}{5}x - 3$

must be part of the graph of the inequality. Therefore, we must select one of the choices with a solid line. Of the two such choices, we can determine which one to select by choosing a test point on one side of the line and substituting the coordinates in the inequality.

The easiest point to select is the origin, or (0,0) . Set x,y = 0 in the inequality:

$y \le - \frac{2}{5}x - 3$

$0 \le - \frac{2}{5} (0) - 3$

$0 \le 0 - 3$

$0 \le - 3$

This is false, so we want the choice that does not include the point (0,0) . The correct choice is the graph:

Axes 1

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GED Math : Geometry and Graphs

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #851 : Geometry And Graphs

Example Question #1 : Graphing Lines

Example Question #851 : Geometry And Graphs

Example Question #851 : Geometry And Graphs

All GED Math Resources

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