Coordinate Geometry: Distance Formula

Find the length of each segment by using the segment as the hypotenuse of a right triangle:
Draw the triangle's legs along the grid lines.
Count the squares on the horizontal and vertical legs.
Use the Pythagorean Theorem to find the length of the hypotenuse.

1

Determine the distance between the two points.
Show your work in the space provided. Write your solution in simplified radical form.

1

Determine the distance between the two points.
Show your work in the space provided. Write your solution in simplified radical form.

Find the length of each segment using the Pythagorean Theorem technique from above.
This time, you must first graph each pair of points on the coordinate plane.

1

Determine the distance between (-9, -6) and (3, 10). Show your work in the space provided.

1

Determine the distance between (1, 3) and (7, 5).
Show your work in the space provided. Write your solution in simplified radical form.

1

Write an expression for the length of the horizontal leg using the x-coordinates.

1

Write an expression for the length of the vertical leg using the y-coordinates.

1

Use your expressions from #5 and #6 along with the Pythagorean Theorem to SELECT ALL TRUE STATEMENTS related to the distance (d) between A(15, 34) and B(42, 70).

1

Let's generalize what you have learned about the distance between two points in a coordinate plane.

Consider the Distance Formula below...

Then SELECT ALL TRUE STATEMENTS related to the distance (d) between A(x_1, y_1) and B(x_2, y_2).

Let's Practice using the Distance Formula!

1

Find the distance between each pair of points using the Distance Formula.
Show all work in the space provided.

1

Find the distance between each pair of points using the Distance Formula.
Show all work in the space provided.

1

Find the distance between each pair of points using the Distance Formula.
Show all work in the space provided. Write your solution in simplified radical form.

1

Find the distance between each pair of points using the Distance Formula.
Show all work in the space provided. Write your solution in simplified radical form.

Determine the distance between the two points.Show your work in the space provided. Write your solution in simplified radical form.

Determine the distance between the two points.Show your work in the space provided. Write your solution in simplified radical form.

Determine the distance between (-9, -6) and (3, 10). Show your work in the space provided.

Determine the distance between (1, 3) and (7, 5).Show your work in the space provided. Write your solution in simplified radical form.

Write an expression for the length of the horizontal leg using the x-coordinates.

Write an expression for the length of the vertical leg using the y-coordinates.

Use your expressions from #5 and #6 along with the Pythagorean Theorem to SELECT ALL TRUE STATEMENTS related to the distance (d) between A(15, 34) and B(42, 70).

Let's generalize what you have learned about the distance between two points in a coordinate plane.Consider the Distance Formula below...Then SELECT ALL TRUE STATEMENTS related to the distance (d) between A(x_1, y_1) and B(x_2, y_2).

Find the distance between each pair of points using the Distance Formula.Show all work in the space provided.

Find the distance between each pair of points using the Distance Formula.Show all work in the space provided.

Find the distance between each pair of points using the Distance Formula.Show all work in the space provided. Write your solution in simplified radical form.

Find the distance between each pair of points using the Distance Formula.Show all work in the space provided. Write your solution in simplified radical form.

Determine the distance between the two points.
Show your work in the space provided. Write your solution in simplified radical form.

Determine the distance between the two points.
Show your work in the space provided. Write your solution in simplified radical form.

Determine the distance between (1, 3) and (7, 5).
Show your work in the space provided. Write your solution in simplified radical form.

Let's generalize what you have learned about the distance between two points in a coordinate plane.

Consider the Distance Formula below...

Then SELECT ALL TRUE STATEMENTS related to the distance (d) between A(x_1, y_1) and B(x_2, y_2).

Find the distance between each pair of points using the Distance Formula.
Show all work in the space provided.

Find the distance between each pair of points using the Distance Formula.
Show all work in the space provided.

Find the distance between each pair of points using the Distance Formula.
Show all work in the space provided. Write your solution in simplified radical form.

Find the distance between each pair of points using the Distance Formula.
Show all work in the space provided. Write your solution in simplified radical form.