### All ACT Math Resources

## Example Questions

### Example Question #1 : How To Find The Endpoints Of A Line Segment

In the standard *(x,y)* coordinate plane, the midpoint of line *XY *is (12, **–**3) and point *X* is located at (3, 4). What are the coordinates of point *Y*?

**Possible Answers:**

(9, **–**7)

(21, **–**10)

(9, 7)

(7.5, 0.5)

(**–**4, 11)

**Correct answer:**

(21, **–**10)

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).

### Example Question #2 : How To Find The Endpoints Of A Line Segment

The midpoint of a line segment is . If one endpoint of the line segment is , what is the other endpoint?

**Possible Answers:**

**Correct answer:**

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 .

### Example Question #3 : How To Find The Endpoints Of A Line Segment

Suppose the midpoint of a line segment is What are the endpoints of the segment?

**Possible Answers:**

**Correct answer:**

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 .

### Example Question #4 : How To Find The Endpoints Of A Line Segment

What is the midpoint of the segment of

between and ?

**Possible Answers:**

**Correct answer:**

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

### Example Question #5 : How To Find The Endpoints Of A Line Segment

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

**Possible Answers:**

**Correct answer:**

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

### Example Question #6 : How To Find The Endpoints Of A Line Segment

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

**Possible Answers:**

**Correct answer:**

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

### Example Question #1 : How To Find The Midpoint Of A Line Segment

What is the coordinate of the point that is halfway between (-2, -4) and (6, 4)?

**Possible Answers:**

(3,1)

(2,2)

(2,0)

(0,2)

**Correct answer:**

(2,0)

The midpoint formula is

### Example Question #1 : How To Find The Midpoint Of A Line Segment

What is the midpoint of MN between the points M(2, 6) and N (8, 4)?

**Possible Answers:**

(5, 5)

(5, 2)

(3, 1)

(2, 1)

(3, 5)

**Correct answer:**

(5, 5)

The midpoint formula is equal to . Add the x-values together and divide them by 2, and do the same for the y-values.

x: (2 + 8) / 2 = 10 / 2 = 5

y: (6 + 4) / 2 = 10 / 2 = 5

The midpoint of MN is (5,5).

### Example Question #2 : How To Find The Midpoint Of A Line Segment

In the standard coordinate plane, what is the midpoint of a line segment that goes from the point (3, 5) to the point (7, 9)?

**Possible Answers:**

(6,6)

(–2, –2)

(7, 5)

(5, 7)

(10,14)

**Correct answer:**

(5, 7)

The midpoint formula is . An easy way to remember this is that finding the midpoint simply requires that you find the averageof the two x-coordinates and the average of the two y-coordinates. In this case, the two x-coordinates are 3 and 7, and the two y-coordinates are 5 and 9. If we substitute these values into the midpoint formula, we get (3 + 7/2), (5 + 9)/2, which equals (5, 7). If you got (–2, –2), you may have subtracted your x and y-coordinates instead of adding. If you got (10,14), you may have forgotten to divide your x and y-coordinates by 2. If you got (6,6), you may have found the average of x_{1 and }y_{2 }and x_{2} and y_{1} instead of keeping the x-coordinates together and the y-coordinates together. If you got (7, 5), you may have switched the x and y-coordinates.

### Example Question #4 : How To Find The Midpoint Of A Line Segment

Find the midpoint of a line segment with endpoints (–1, 4) and (3, 6).

**Possible Answers:**

(4, 5)

(5, 1)

(3, 2)

(1, 5)

**Correct answer:**

(1, 5)

The formula for midpoint = (x_{1} + x_{2})/2, (y_{1} + y_{2})/2. Substituting in the two x coordinates and two y coordinates from the endpoints, we get (–1 + 3)/2.

(4 + 6)/2 or (1, 5) as the midpoint.

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