### All SAT Math Resources

## Example Questions

### Example Question #11 : Distance Formula

Find the Distance of the line shown below:

**Possible Answers:**

**Correct answer:**

The distance formula is . In the graph shown above the coordinates are and . When you plug the coordinates into the equation you get:

, which then simplifies to

, because is a prime number there is no need to simplify.

### Example Question #12 : Distance Formula

The endpoints of the diameter of a circle are located at (0,0) and (4, 5). What is the area of the circle?

**Possible Answers:**

**Correct answer:**

First, we want to find the value of the diameter of the circle with the given endpoints. We can use the distance formula here:

If the diameter is , then the radius is half of that, or .

We can then plug that radius value into the formula for the area of a circle.

.

### Example Question #11 : How To Find The Length Of A Line With Distance Formula

What is the distance between the origin and the point ?

**Possible Answers:**

None of the given answers.

**Correct answer:**

The distance between two points and is given by the Distance Formula:

Let and . Substitute these values into the Distance Formula.

To simplify this square root, find a common denominator between the two terms.

Both 4 and are perfect squares, so we can take their square roots to find

The distance between our two points is .

### Example Question #14 : Distance Formula

One long line segment stretches from to . Within that line segment is another, shorter segment that spans from to . What is the distance between the two points on the shorter line segment?

**Possible Answers:**

**Correct answer:**

The distance between two points and is given by the following formula:

Let and let . When we plug these two coordinates into the equation we get:

### Example Question #15 : Distance Formula

Find the distance from the center of the given circle to the point .

**Possible Answers:**

**Correct answer:**

Remember that the general equation of a circle with center and radius is .

With this in mind, the center of our circle is . To find the distance from this point to , we can use the distance formula.

### Example Question #16 : Distance Formula

The following points represent the vertices of a box. Find the length of the box's diagonal.

**Possible Answers:**

None of the given answers

**Correct answer:**

To solve this problem let's choose two vertices that lie diagonally from one another. Let's choose and .

We can plug these two points into the Distance Formula, and that will give us the length of the box's diagonal.

### Example Question #17 : Distance Formula

What is the length of the line between the points and ?

**Possible Answers:**

**Correct answer:**

Step 1: We need to recall the distance formula, which helps us calculate the length of a line between the two points.

The formula is: , where distance and are my two points.

Step 2: We need to identify .

Step 3: Substitute the values in step 2 into the formula:

Step 4: Start evaluating the parentheses:

Step 5: Evaluate the exponents inside the square root

Step 6: Add the inside:

Step 7: We need to evaluate in a calculator

### Example Question #18 : Distance Formula

Give the length, in terms of , of a segment on the coordinate plane whose endpoints are and .

**Possible Answers:**

**Correct answer:**

The length of a segment with endpoints and can be calculated using the distance formula:

Setting and and substituting:

The binomials can be rewritten using the perfect square trinomial pattern:

Simplify and collect like terms:

### Example Question #19 : Distance Formula

In terms of , give the length of a segment on the coordinate plane with endpoints and .

**Possible Answers:**

**Correct answer:**

The length of a segment with endpoints and can be calculated using the distance formula:

Setting and , and substituting:

The binomials can be rewritten using the perfect square trinomial pattern:

Simplify and collect like terms:

### Example Question #20 : Distance Formula

Give the length, in terms of , of a line segment on the coordinate plane whose endpoints are and .

**Possible Answers:**

**Correct answer:**

The length of a segment with endpoints can be calculated using the distance formula

Substituting , and simplifying"

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