Question 1

Which of the following ordered pairs is located in Quadrant II of the Cartesian plane?

Accepted Answer

$$(-4, 5)$$

Question 2

Given the equation $$y = 2x^2$ + 3x - 7$$, what is the y-intercept of the graph?

Accepted Answer

$$(0, -7)$$

Question 3

If the midpoint of a line segment joining points $$A(4, -3)$$ and $$B(4, 5) is$$ $$M(x, y)$$, what are the coordinates of $$M$$?

Accepted Answer

$$(4, 1)$$

Question 4

Which formula correctly gives the distance between two points $$A(x_1$, y_1$)$$ and $$B(x_2$, y_2$) in $$the plane?

Accepted Answer

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

Question 5

A point $$P$$ has coordinates $$(x, y)$$ and lies 5 units away from the point $$(-3, 3). If$$ $$x = 1$$, what are the possible values of $$y$$?

Accepted Answer

$$y = 6 or$$ $$y = 0$$

Question 6

Which of the following statements about the Cartesian plane is TRUE?

Accepted Answer

The origin divides the plane into four quadrants labeled I, II, III, and IV.

Question 7

Given the equation $$y = x^2$ - 4x - 21$$, what are the $$x-$$intercepts?

Accepted Answer

$$(7, 0)$$ and $$(-3, 0)$$

Question 8

If a line segment has endpoints $$(7, 3)$$ and $$(x, y)$$, and its midpoint is $$(7, \frac{1}{2})$$, what is the value of $$y$$?

Accepted Answer

$$y = -2$$

Question 9

A chemical sensor is placed at $$(2, 5) in a $$lab. Another sensor must be exactly 10 units away. Which of the following could be the coordinates of the second sensor?

Accepted Answer

$$(2, -5)$$

Question 10

Which of the following best describes an $$x-$$intercept?

Accepted Answer

A point where the graph touches or crosses the $$x-$$axis.

Question 11

A medical researcher plots the location of two samples at $$(1, 2)$$ and $$(4, 6). $$What is the distance between the samples?

Accepted Answer

$$5$$

Question 12

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

Accepted Answer

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

Question 13

A biologist marks two trees at $$(0, 0)$$ and $$(6, 8). $$What is the straight-line distance between the trees?

Accepted Answer

$$10$$

Question 14

Which of the following is NOT a correct way to represent an ordered pair?

Accepted Answer

$$(y, x)$$

Question 15

A city planner wants to place a park at the midpoint between two intersections at $$(2, 7)$$ and $$(10, 3). $$What are the coordinates of the park?

Accepted Answer

$$(6, 5)$$

Question 16

If the equation of a line is $$y = 3x + 2$$, what is the $$y-$$intercept?

Accepted Answer

$$(0, 2)$$

Question 17

A runner starts at $$(0, 0)$$ and runs to $$(5, 12). $$What is the total distance covered?

Accepted Answer

$$13$$

Question 18

Which of the following points lies on the graph of $$y = x^2$ - 4x - 21$$?

Accepted Answer

$$(7, 0)$$

Question 19

A surveyor needs to find the midpoint between $$(8, 2)$$ and $$(4, 10). $$What is the midpoint?

Accepted Answer

$$(6, 6)$$

The Cartesian Plane: Ordered Pairs, Intercepts, Midpoints, and Distance

Guida di studio - Domande di pratica

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