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ACT Math : Coordinate Geometry

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Example Questions

Example Question #631 : Geometry

The coordinates of the endpoints of $\overline{CD}$ , in the standard (x,y) coordinate plane, are (-2,-1) and (7,1) . What is the -coordinate of the midpoint of $\overline{CD}$ ?

Possible Answers:

2.5

Correct answer:

2.5

Explanation:

To answer this question, we need to find the midpoint of $\overline{CD}$ .

To find how far the midpoint of a line is from each end, we use the following equation:

$midpoint \:distance=\frac{x_{2}-x_{1}}{2}, \frac{y_{2}-y_{1}}{2}$

$x_{2}$ and $y_{2}$ are taken from the x,y value of the second point and $x_{1}$ and $y_{1}$ are taken from the x,y value of the first point. Therefore, for this data:

$midpoint \:distance=\frac{x_{2}-x_{1}}{2}, \frac{y_{2}-y_{1}}{2}=\frac{7-(-2)}{2}, \frac{1-(-1)}{2}$

We can then solve:

$\frac{7-(-2)}{2}, \frac{1-(-1)}{2}=\frac{9}{2},\frac{2}{2}=4.5,1$

Therefore, our midpoint is 4.5 units between each endpoint's value and unit between each endpoint's value. To find out the location of the midpoint, we subtract the midpoint distance from the $x_{2},y_{2}$ point. (In this case it's the point 7,1 .) Therefore:

7-4.5= 2.5

1-1=0

So the midpoint is located at 2.5,0

The question asked us what the -coordinate of this point was. Therefore, our answer is 2.5 .

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Example Question #632 : Geometry

Following the line $y=\frac{4}{3}x-4$ , what is the distance from the the point where x=1 to the point where x=4 ?

Possible Answers:

$\frac{4}{3}$

$\frac{3}{4}$

Correct answer:

Explanation:

The first step is to find the y-coordinates for the two points we are using. To do this we plug our x-values into the equation. Where x=1 , we get $\frac{4}{3}-4=-\frac{8}{3}$ , giving us the point $\left(1,-\frac{8}{3}\right)$ . Where x=4 , we get $\frac{16}{3}-4=\frac{4}{3}$ , giving us the point $\left(4,\frac{4}{3}\right)$ .

We can now use the distance formula: $d=\sqrt{(x_{1}-x_{2})^2+(y_{1}-y_{2})^2}$ .

Plugging in our points gives us $d=\sqrt{(1-4)^2+\left(-\frac{8}{3}-\frac{4}{3}\right)^2}=\sqrt{(-3)^2+(-4)^2}=\sqrt{25}=5$

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Example Question #11 : Coordinate Geometry

Which of the following is the slope-intercept form of 10x+2y-4=0 ?

Possible Answers:

y = 5x - 2

y = 5x + 2

y = -5x -2

y = -5x + 2

2y = -10x + 4

Correct answer:

y = -5x + 2

Explanation:

To answer this question, we must put the equation into slope-intercept form, meaning we must solve for . Slope-intercept form follows the format y = mx + b where is the slope and is the intercept.

Therefore, we must solve the equation so that is by itself. First we add to both sides so that we can start to get by itself:

$10x+2y-4 +4=0+4\rightarrow 10x+2y=4$

Then, we must subtract 10x from both sides:

$10x+2y -10x=4-10x\rightarrow 2y=-10x+4$

We then must divide each side by

$\frac{2y}{2}=\frac{-10x+4}{2}\rightarrow y=-5x+2$

Therefore, the slope-intercept form of the original equation is y=-5x+2 .

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ACT Math : Coordinate Geometry

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #631 : Geometry

Example Question #632 : Geometry

Example Question #11 : Coordinate Geometry

All ACT Math Resources

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