Question

what triangle is formed by the points (3,2), (4,7), and (5,6)? triangle a triangle d triangle c triangle b

Explanation:

Step1: Identify the points

Let the points be \( A(3,2) \), \( B(4,7) \), and \( C(5,6) \). Wait, no, we need to check which triangle's vertices match these points. Looking at the first graph, the bottom point is \( (3,2) \), then \( (4,7) \) and \( (5,6) \). Let's check the coordinates of triangle A: the bottom vertex is \( (3,2) \), one upper vertex is \( (4,7) \), and the other is \( (5,6) \)? Wait, no, let's list the coordinates of each triangle's vertices.

Looking at the first graph (left):

• Triangle A: vertices at \( (3,2) \), \( (4,7) \), \( (5,6) \)? Wait, no, the bottom point is \( (3,2) \), then \( (4,7) \) (point A) and \( (5,6) \)? Wait, the x-coordinates of the given points are 3,4,5. So the bottom point is x=3 (y=2), then x=4 (y=7) and x=5 (y=6). So in the left graph, triangle A has vertices at (3,2), (4,7), and (5,6)? Wait, no, the left graph's triangle A: the bottom vertex is (3,2), then (4,7) (red) and (5,6)? Wait, the blue points: (5,6) is a blue point, (4,7) is red (A), (3,2) is the bottom. So triangle A is formed by (3,2), (4,7), (5,6). Let's confirm the other triangles:

Triangle B: vertices at (3,2), (7,4), (6,5)? No, x-coordinates 3,7,6 – not 3,4,5.

Triangle C (right graph): vertices at (2,2), (4,7), (5,6)? No, bottom vertex is (2,2).

Triangle D (right graph): vertices at (2,2), (7,5), (8,4)? No.

So the given points (3,2), (4,7), (5,6) match the vertices of triangle A.

Step2: Confirm the coordinates

Given points: (3,2), (4,7), (5,6). In the left graph, triangle A has a vertex at (3,2) (bottom), (4,7) (top left), and (5,6) (top right). So these coordinates match.

Answer:

triangle A