# ACT Math : Coordinate Geometry

## Example Questions

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### Example Question #11 : Coordinate Geometry

The coordinates of the endpoints of , in the standard  coordinate plane, are  and . What is the -coordinate of the midpoint of ?

Explanation:

To answer this question, we need to find the midpoint of .

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

and  are taken from the  value of the second point and  and  are taken from the  value of the first point. Therefore, for this data:

We can then solve:

Therefore, our midpoint is  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  point. (In this case it's the point .) Therefore:

So the midpoint is located at

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

### Example Question #12 : Coordinate Geometry

Following the line , what is the distance from the the point where  to the point where ?

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 , we get , giving us the point . Where , we get , giving us the point .

We can now use the distance formula: .

Plugging in our points gives us

### Example Question #13 : Coordinate Geometry

Which of the following is the slope-intercept form of ?

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  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:

Then, we must subtract  from both sides:

We then must divide each side by

Therefore, the slope-intercept form of the original equation is .

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