Question 1

Which of the following is the correct formula for finding the distance between two points $$A(x_1$, y_1$)$$ and $$B(x_2$, y_2$) in $$the rectangular coordinate system?

Accepted Answer

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

Question 2

Given the points $$P(2, 3)$$ and $$Q(8, 11)$$, what is the distance between them?

Accepted Answer

$$\sqrt{100} = 10$$

Question 3

What is the midpoint of the line segment joining the points $$A(-4, 7)$$ and $$B(2, -1)$$?

Accepted Answer

$$(-1, 3)$$

Question 4

Which equation represents a line passing through the point $$(0, 5)$$ with a slope of $$-2$$?

Accepted Answer

$$y = -2x + 5$$

Question 5

A biologist tracks the movement of a tagged animal from $$(1, 2) to$$ $$(7, 14). $$What is the animal's straight-line displacement?

Accepted Answer

$$\sqrt{36 + 144} = \sqrt{180}$$

Question 6

If the midpoint of a segment is $$(4, -3)$$ and one endpoint is $$(2, 1)$$, what is the other endpoint?

Accepted Answer

$$(6, -7)$$

Question 7

Which of the following points lies on the graph of the equation $$y = 3x - 4$$?

Accepted Answer

$$(1, -1)$$

Question 8

A city planner wants to build a road directly between two intersections at $$(5, 8)$$ and $$(13, 20). $$What is the midpoint of the road?

Accepted Answer

$$(9, 14)$$

Question 9

Which of the following is the equation of a line parallel to $$y = -\frac{1}{2}x + 3$$ and passing through $$(4, -2)$$?

Accepted Answer

Question 10

A drone flies from $$(0, 0) to$$ $$(6, 8). $$What is the distance traveled by the drone?

Accepted Answer

$$10$$

Question 11

If the equation of a line is $$y = 4x - 7$$, what is the $$y-$$intercept?

Accepted Answer

$$-7$$

Question 12

Which of the following equations represents a vertical line passing through $$(3, -2)$$?

Accepted Answer

$$x = 3$$

Question 13

A medical researcher records the locations of two hospitals at $$(10, 5)$$ and $$(4, 13). $$What is the distance between the hospitals?

Accepted Answer

$$\sqrt{36 + 64} = 10$$

Question 14

Which of the following is the correct formula for the midpoint of a segment with endpoints $$(x_1$, y_1$)$$ and $$(x_2$, y_2$)$$?

Accepted Answer

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

Question 15

A chemist marks two points on a rectangular tray at $$(1, 4)$$ and $$(7, 10). $$What is the midpoint between these two points?

Accepted Answer

$$(4, 7)$$

Question 16

Which of the following points does NOT lie on the line $$y = 2x - 3$$?

Accepted Answer

$$(3, 3)$$

Question 17

A delivery truck travels from warehouse $$A(3, 7) to $$warehouse $$B(11, 15). $$What is the straight-line distance between the warehouses?

Accepted Answer

$$\sqrt{64 + 64} = \sqrt{128}$$

Question 18

If a line passes through $$(2, 5)$$ and $$(6, 13)$$, what is its slope?

Accepted Answer

$$2$$

Question 19

Which of the following equations represents a line with slope $$3$$ and $$y-$$intercept $$-2$$?

Accepted Answer

$$y = 3x - 2$$

Question 20

A botanist records the growth of a plant at two points: $$(0, 2)$$ and $$(4, 10). $$What is the average rate of growth (slope) between these points?

Accepted Answer

$$2$$

Graphing, Distance, and Midpoint in the Rectangular Coordinate System

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