which of these statements accurately describe(s) the points shown?

a. point v has coordinates $(-2, -1)$ and is in quadrant 3.
b. point w has coordinates $(2, -3)$ and is in quadrant 2.
c. a line connecting these points would have a slope of $-2$.

- a, b, and c
- a and b
- b only
- a only

Question

which of these statements accurately describe(s) the points shown?

a. point v has coordinates $(-2, -1)$ and is in quadrant 3.
b. point w has coordinates $(2, -3)$ and is in quadrant 2.
c. a line connecting these points would have a slope of $-2$.

- a, b, and c
- a and b
- b only
- a only

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Coordinate Plane", "Quadrants", "Slope Formula" ], "new_concepts": [], "current_concepts": [ "Coordinate Plane", "Quadrants", "Slope Formula" ] } ## Determine coordinates and quadrants of points v and w $$ \begin{aligned} &v = (-2, -1) \quad \text{in Quadrant 3 (both coordinates negative)} \ &w = (2, -3) \quad \text{in Quadrant 4 (positive } x \text{, negative } y\text{)} \end{aligned} $$ ## Calculate the slope of the line connecting v and w $$ \begin{aligned} &m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-3 - (-1)}{2 - (-2)} = \frac{-2}{4} = -\frac{1}{2} \end{aligned} $$ ## Evaluate statements A, B, and C $$ \begin{aligned} &\text{Statement A: } v = (-2, -1) \text{ in Quadrant 3 is True.} \ &\text{Statement B: } w = (2, -3) \text{ in Quadrant 2 is False (it is in Quadrant 4).} \ &\text{Statement C: Slope is } -2 \text{ is False (slope is } -\frac{1}{2}\text{).} \end{aligned} $$

A, B, and C

A and B

B only

A only

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Coordinate Plane" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Determine coordinates and quadrants of points v and w

Calculate the slope of the line connecting v and w

Evaluate statements A, B, and C

Answer: