How to find the length of a line with distance formula - PSAT Math

AB = 10 ’

BC = AC – AB = 25’ – 10’ = 15’

CD = 2 * AB = 2 * 10’ = 20 ’

AD = AB + BC + CD = 10’ + 15’ + 20’ = 45’

Let P1 = (1, 4) and P2 = (5, 1)

Substitute these values into the distance formula:

The distance formula is an application of the Pythagorean Theorem: a2 + b2 = c2

The answer is 10. Use the distance formula between 2 points, or draw a right triangle with legs length 6 and 8 and use the Pythagorean Theorem.

Plug the points into the distance formula and simplify:

distance2 = (_x_2 – _x_1)2 + (_y_2 – _y_1)2 = (7 – 3)2 + (2 – 12)2 = 42 + 102 = 116

distance = √116 = √(4 * 29) = 2√29

The distance formula is .

Plug in with each of the answer choices and solve.

Plug in :

This is therefore the correct answer choice.

Let and and use the distance formula:

The distance between 2 points is found using the distance or Pythagorean Theorem. Because values are squared in the formula, distance can never be a negative value.

The formula for the distance between two points is .

Plug in the points:

Each part of the problem gives you 2 out of the 3 pieces of the rate/time/distance relationship, thus allowing you to find the third (if needed) by using the equation:

The problem is otherwise an application of geometry and the distance formula. We need to find the distance between 2 points, but we need to go step-by-step to find out where the final point is. The first two steps are relatively easy to follow. He travels 30 miles north. Now he turns west and travels for 40 minutes at 40 mph. This is of an hour, so we have . Thus if we are looking at standard Cartesian coordinates (starting at the origin), we are now at the point .

We are now on the last step: 40 miles northeast. We need to decipher this into - and - coordinate changes. To do this, we think of a triangle. Because we are moving directly northeast, this is a 45 degree angle to the horizontal. We can thus imagine a 45-45-90 triangle with a hypotenuse of 40. Now using the relationships on triangles we have:

So the final step moves us up and to the right. Moving this way from the point leaves us at:

Using the distance formula for this point from the origin gives us a distance of ~58 miles.

Now for the time. We traveled 30 miles at 40 mph. This means we traveled for hours or 45 minutes.

We then traveled 40 mph for 40 minutes. Increasing our total time traveled to 85 minutes.

Finally, we traveled 40 miles in 25 minutes, leaving our total time traveled at 110 minutes. Returning to hours, we have hours or 1.83 hours.

Our final average speed traveled is then:

The closest answer to this value is 32 mph.

To find the distance between two points such as these, plot them on a graph.

Then, find the distance between the units of the points, which is 12, and the distance between the points, which is 5. The represents the horizontal leg of a right triangle and the represents the vertial leg of a right triangle. In this case, we have a 5,12,13 right triangle, but the Pythagorean Theorem can be used as well.

AB = 10 ’

BC = AC – AB = 25’ – 10’ = 15’

CD = 2 * AB = 2 * 10’ = 20 ’

AD = AB + BC + CD = 10’ + 15’ + 20’ = 45’

Let P1 = (1, 4) and P2 = (5, 1)

Substitute these values into the distance formula:

The distance formula is an application of the Pythagorean Theorem: a2 + b2 = c2

The answer is 10. Use the distance formula between 2 points, or draw a right triangle with legs length 6 and 8 and use the Pythagorean Theorem.

Plug the points into the distance formula and simplify:

distance2 = (_x_2 – _x_1)2 + (_y_2 – _y_1)2 = (7 – 3)2 + (2 – 12)2 = 42 + 102 = 116

distance = √116 = √(4 * 29) = 2√29

The distance formula is .

Plug in with each of the answer choices and solve.

Plug in :

This is therefore the correct answer choice.

Let and and use the distance formula:

The distance between 2 points is found using the distance or Pythagorean Theorem. Because values are squared in the formula, distance can never be a negative value.

The formula for the distance between two points is .

Plug in the points:

Each part of the problem gives you 2 out of the 3 pieces of the rate/time/distance relationship, thus allowing you to find the third (if needed) by using the equation:

The problem is otherwise an application of geometry and the distance formula. We need to find the distance between 2 points, but we need to go step-by-step to find out where the final point is. The first two steps are relatively easy to follow. He travels 30 miles north. Now he turns west and travels for 40 minutes at 40 mph. This is of an hour, so we have . Thus if we are looking at standard Cartesian coordinates (starting at the origin), we are now at the point .

We are now on the last step: 40 miles northeast. We need to decipher this into - and - coordinate changes. To do this, we think of a triangle. Because we are moving directly northeast, this is a 45 degree angle to the horizontal. We can thus imagine a 45-45-90 triangle with a hypotenuse of 40. Now using the relationships on triangles we have:

So the final step moves us up and to the right. Moving this way from the point leaves us at:

Using the distance formula for this point from the origin gives us a distance of ~58 miles.

Now for the time. We traveled 30 miles at 40 mph. This means we traveled for hours or 45 minutes.

We then traveled 40 mph for 40 minutes. Increasing our total time traveled to 85 minutes.

Finally, we traveled 40 miles in 25 minutes, leaving our total time traveled at 110 minutes. Returning to hours, we have hours or 1.83 hours.

Our final average speed traveled is then:

The closest answer to this value is 32 mph.