IM 6.7.14 Lesson: Distances on a Coordinate Plane

Plot points in your assigned quadrant and label them with their coordinates.

Write the coordinates of each point shown in the graph below. [br][list][*][math]A=[/math][br][/*][*][math]B=[/math][br][/*][*][math]C=[/math][br][/*][*][math]D=[/math][br][/*][*][math]E=[/math][br][/*][/list]

Answer these questions for each pair of points.

[list][*]How are the coordinates the same? How are they different?[/*][*]How far away are they from the y-axis? To the left or to the right of it?[/*][*]How far away are they from the x-axis? Above or below it?[/*][/list][br][math]A[/math] and [math]B[/math]

[math]B[/math] and [math]D[/math]

[math]A[/math] and [math]D[/math]

Point F has the same coordinates as point C, except its y-coordinate has the opposite sign. Plot point F on the coordinate plane and label it with its coordinates.

How far away are[math]F[/math] and [math]C[/math] from the [math]x[/math]-axis?[br]

What is the distance between [math]F[/math] and [math]C[/math]?

Point G has the same coordinates as point E, except its x-coordinate has the opposite sign. Plot point G on the coordinate plane and label it with its coordinates.

How far away are [math]G[/math] and [math]E[/math] from the [math]y[/math]-axis?

What is the distance between [math]G[/math] and [math]E[/math]?

Point [math]H[/math] has the same coordinates as point [math]B[/math], except both of its coordinates have the opposite signs. In which quadrant is point [math]H[/math]?

Label each point with its coordinates.

Find the distance between each of the following pairs of points.

Point [math]B[/math] and [math]C[/math]

Point [math]D[/math] and [math]B[/math]

Point [math]D[/math] and [math]E[/math]

Which of the points are 5 units from [math]\left(-1.5,-3\right)[/math]?

Which of the points are 2 units from [math]\left(0.5,-4.5\right)[/math]?

Plot a point that is both 2.5 units from A and 9 units from E. Label that point F and write down its coordinates.

Priya says, “There are exactly four points that are 3 units away from [math]\left(-5,0\right)[/math].” Lin says, “I think there are a whole bunch of points that are 3 units away from [math]\left(-5,0\right)[/math].”[br][br]Do you agree with either of them? Explain your reasoning.