Question 1

Which formula is used to find the distance between two points $$A(x_1$, y_1$)$$ and $$B(x_2$, y_2$) in $$the Cartesian plane?

Accepted Answer

$$d = \sqrt{(x_2$ - x_1$)^2$$ + ($$y_2$$ - $$y_1)^2$}$$

Question 2

Find the distance between the points $$(0, 1)$$ and $$(3, 5).$$

Accepted Answer

$$5$$

Question 3

Given points $$A = (-2, 1)$$, $$B = (2, 3)$$, and $$C = (3, 1)$$, which of the following correctly shows that these points form a right triangle using the Pythagorean Theorem?

Accepted Answer

$$AB^2$$ + $$AC^2$$ = $$BC^2$$

Question 4

What is the area of the triangle with vertices $$A = (-2, 1)$$, $$B = (2, 3)$$, and $$C = (3, 1)$$?

Accepted Answer

$$6$$

Question 5

Which formula is used to find the midpoint $$M of a $$line segment joining points $$P_1$$($$x_1$$, $$y_1$$)$$ and P_2$(x_2$, y_2$)$$?

Accepted Answer

$$M = \left( \frac{x_1$ + x_2$}{2}, \frac{y_1$ + y_2$}{2} \right)$$

Question 6

Find the midpoint of the segment joining $$P_1 = (2$$, -3)$$ and P_2$ = (4, 2).$$

Accepted Answer

$$(3, -0.5)$$

Question 7

If the midpoint of the segment from $$P_1 = (-3$$, 6)$$ to P_2$ is (-1$$, 4)$$, what are the coordinates of P_2$?

Accepted Answer

$$(1, 2)$$

Question 8

A cell phone tower is located at $$(2, 5). A $$technician must install a backup generator exactly halfway between the tower and the maintenance office at $$(8, 1). $$What are the coordinates where the generator should be installed?

Accepted Answer

$$(5, 3)$$

Question 9

Find all points with $$x = 3$$ that are 13 units from $$(-2, -1).$$

Accepted Answer

$$(3, 12)$$ and $$(3, -14)$$

Question 10

A city park is represented by the points $$(1, 2)$$ and $$(7, 8) on a $$map. What is the length of the diagonal across the park?

Accepted Answer

$$6\sqrt{2}$$

Question 11

Which of the following best describes the Cartesian coordinate system?

Accepted Answer

A system that uses two perpendicular number lines to locate points in a plane.

Question 12

A drone flies from $$(4, 7) to$$ $$(10, 1). $$What is the straight-line distance it travels?

Accepted Answer

$$6\sqrt{2}$$

Question 13

If the endpoints of a diameter of a circle are $$(2, 3)$$ and $$(8, 11)$$, what is the center of the circle?

Accepted Answer

$$(5, 7)$$

Question 14

A wildlife biologist marks two locations of rare plants at $$(5, -2)$$ and $$(-3, 4). $$What is the distance between the two locations?

Accepted Answer

$$10$$

Question 15

Which of the following is NOT a correct application of the distance formula?

Accepted Answer

Finding the midpoint between two points.

Distance and Midpoint Formulas in Analytic Geometry

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