Answer:

CD = √[(7 - (-2))² + (1 - y)²] = √[(9)² + (1 - y)²] = √(81 + (1 - y)²)

√(81 + (1 - y)²) = √58

81 + (1 - y)² = 58

(1 - y)² = -23

Step-by-step explanation:

The distance formula for finding the distance between two points in a coordinate plane is:

d = √[(x2 - x1)² + (y2 - y1)²]

We are given that C(7, 1) and D(-2, y) and that CD = √58. We want to find the value of y.

Using the distance formula, we can write:

CD = √[(7 - (-2))² + (1 - y)²] = √[(9)² + (1 - y)²] = √(81 + (1 - y)²)

We are told that CD = √58, so we can set these two expressions equal to each other and solve for y:

√(81 + (1 - y)²) = √58

Square both sides:

81 + (1 - y)² = 58

Simplify:

(1 - y)² = 58 - 81 = -23

Since a squared value can never be negative, this equation has no real solutions. Therefore, there is no value of y that makes CD equal to √58