Question

Use the give coordinate to determine triangle ABC is congruent to triangle DEF

A(1, 1) B(4,0) C(7,5)
D(-4,-5) E (6,-6) F(9,-1)

Answer 1

By calculating the lengths of the sides of both triangles using the distance formula, we can see that none of the side lengths of triangles ABC and DEF match, indicating the two triangles are not congruent.

Step-by-step explanation:

To determine if triangle ABC is congruent to triangle DEF, we need to use the given coordinates to calculate the lengths of the sides of each triangle and then compare them. We can do this using the distance formula for any two points (x1, y1) and (x2, y2), which is √((x2-x1)² + (y2-y1)²).

First, let's calculate the lengths of the sides of triangle ABC:

• AB = √((4 - 1)² + (0 - 1)²) = √3
• BC = √((7 - 4)² + (5 - 0)²) = √34
• CA = √((1 - 7)² + (1 - 5)²) = √52

Next, we calculate the lengths of triangle DEF:

• DE = √((-4 - 6)² + (-5 - (-6))²) = √(100 + 1) = √101
• EF = √((9 - 6)² + (-1 - (-6))²) = √18
• FD = √((-4 - 9)² + (-5 - (-1))²) = √170

Comparing the side lengths, we see that no sides of triangle ABC are equal in length to sides of triangle DEF, thus necessarily the two triangles cannot be congruent.