what is the area of the triangle in the diagram?

$\frac{1}{2}(x_1 - y_1)(x_2 - y_1)$

Question

what is the area of the triangle in the diagram?

$\frac{1}{2}(x_1 - y_1)(x_2 - y_1)$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Coordinate Geometry", "Triangle Area Formula" ], "current_concepts": [ "Coordinate Geometry", "Triangle Area Formula" ] } ## Identify the base and height of the triangle $$ \begin{aligned} &\text{Vertices: } (x_1, y_1), (x_2, y_1), (0, 0)\ &\text{Base } (b) = x_2 - x_1\ &\text{Height } (h) = y_1 \end{aligned} $$ ## Apply the triangle area formula $$ \begin{aligned} &\text{Area} = \frac{1}{2} \cdot \text{base} \cdot \text{height}\ &\text{Area} = \frac{1}{2}(x_2 - x_1)y_1 \end{aligned} $$

(A) $\frac{1}{2}(x_2 - x_1)y_1$

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

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QUESTION IMAGE

Question

Explanation:

Identify the base and height of the triangle

Apply the triangle area formula

Answer: