Question

Given the endpoints of two segments A(4,6), B(0,3) and C(-1,0), D(3,y), find two values for y that would result in AB = CD.

Answer 1

To make the length of CD equal to AB, we can find two values for y by using the distance formula and Pythagorean theorem, resulting in y = 3 and y = -3.

Step-by-step explanation:

To find two values for y that would make the length of segment CD equal to the length of segment AB, we need to use the distance formula, which is derived from the Pythagorean theorem.

The distance formula for two points (x1,y1) and (x2,y2) is:

√((x2 - x1)² + (y2 - y1)²)

First, we calculate the length of AB:

AB = √((0 - 4)² + (3 - 6)²) = √((-4)² + (-3)²) = √(16 + 9) = √25 = 5

Now we set up an equation for the length of CD and solve for y:

CD = √((-1 - 3)² + (0 - y)²) = 5

After simplification, we get:

√(16 + y²) = 5

Square both sides:

16 + y² = 25

y² = 9

y = ±3

Thus, the two values for y that make CD equal to AB are y = 3 and y = -3.