Asked by t
Use the image to answer the question.
A triangle is graphed by joining three plotted points on a coordinate plane. The x-axis ranges from negative 6 to 10 in increments of 2 and the y-axis ranges from negative 4 to 10 in increments of 2.
Amaury draws an acute triangle on the coordinate grid. He finds the area of the triangle by drawing a rectangle that circumscribes the triangle and forming right triangles. Show the steps Amaury must take to find the area of the triangle. What is the area of the triangle in square units?
All Answers 1
Answered by
GPT-5 mini
AI
I can’t see the image you mentioned. Could you upload it or tell me the coordinates of the three vertices of the triangle?
Meanwhile, here are the clear steps Amaury would use with the circumscribing rectangle method so you can apply them once you provide the picture or coordinates:
1. Identify the triangle’s vertices A(x1,y1), B(x2,y2), C(x3,y3).
2. Find the axis-aligned bounding rectangle that circumscribes the triangle:
- left = min(x1,x2,x3), right = max(x1,x2,x3)
- bottom = min(y1,y2,y3), top = max(y1,y2,y3)
- rectangle width = right − left, height = top − bottom
- rectangle area = width × height
3. Inside that rectangle the triangle plus three (or fewer) right triangles fill the rectangle. Compute the areas of the right triangles formed in the three corners outside the triangle. Each such right triangle area = (horizontal leg × vertical leg) / 2, where the legs are the horizontal and vertical distances from a triangle vertex to the rectangle edge at that corner.
4. Subtract the sum of those outside right-triangle areas from the rectangle area:
triangle area = rectangle area − (area of corner triangle 1 + area of corner triangle 2 + area of corner triangle 3)
(If one corner contains a triangle of zero area because a vertex lies on that rectangle corner or side, include zero.)
5. Alternatively (and often simpler), if you can identify a horizontal base and its corresponding vertical height, use area = 1/2 × base × height, or use the shoelace formula with the three vertices.
If you upload the image or tell me the three vertex coordinates, I’ll carry out these steps and give the numerical area.
Meanwhile, here are the clear steps Amaury would use with the circumscribing rectangle method so you can apply them once you provide the picture or coordinates:
1. Identify the triangle’s vertices A(x1,y1), B(x2,y2), C(x3,y3).
2. Find the axis-aligned bounding rectangle that circumscribes the triangle:
- left = min(x1,x2,x3), right = max(x1,x2,x3)
- bottom = min(y1,y2,y3), top = max(y1,y2,y3)
- rectangle width = right − left, height = top − bottom
- rectangle area = width × height
3. Inside that rectangle the triangle plus three (or fewer) right triangles fill the rectangle. Compute the areas of the right triangles formed in the three corners outside the triangle. Each such right triangle area = (horizontal leg × vertical leg) / 2, where the legs are the horizontal and vertical distances from a triangle vertex to the rectangle edge at that corner.
4. Subtract the sum of those outside right-triangle areas from the rectangle area:
triangle area = rectangle area − (area of corner triangle 1 + area of corner triangle 2 + area of corner triangle 3)
(If one corner contains a triangle of zero area because a vertex lies on that rectangle corner or side, include zero.)
5. Alternatively (and often simpler), if you can identify a horizontal base and its corresponding vertical height, use area = 1/2 × base × height, or use the shoelace formula with the three vertices.
If you upload the image or tell me the three vertex coordinates, I’ll carry out these steps and give the numerical area.
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.