Question

Segment AB has point A located at (5, 4). If the distance from A to B is 7 units, which of

the following could be used to calculate the coordinates for point B?
A. 7- V(x + 4)2 + (y+5)2
B. 7 = V(x+5)2 + (y+4)
C. 7 = V(x - 4)2 +(y – 5)
D. 7 = V(x - 5)2 + (y-4)

Answer 1

Segment AB has point A located at (5, 4). If the distance from A to B is 7 units, which of
the following could be used to calculate the coordinates for point B?
A. 7- V(x + 4)2 + (y+5)2
B. 7 = V(x+5)2 + (y+4)
C. 7 = V(x - 4)2 +(y – 5)
D. 7 = V(x - 5)2 + (y-4)✅

Answer 2

The correct option to calculate the coordinates for point B, given point A at (5, 4) and the distance AB being 7 units, is D: 7 = √((x - 5)^2 + (y - 4)^2), based on the Pythagorean theorem.

Step-by-step explanation:

To calculate the coordinates for point B given that segment AB has a distance of 7 units and point A is located at (5, 4), you would use the distance formula derived from the Pythagorean theorem.

The distance formula is given by D = √((x2 - x1)^2 + (y2 - y1)^2), where D is the distance between two points, and (x1, y1) and (x2, y2) are the coordinates of these points. In this problem, A is at (5, 4) and the distance D is 7 units.

The correct formula that correlates with these given values for calculating the coordinates of point B is: 7 = √((x - 5)^2 + (y - 4)^2), which is option D.

This expression squares the difference between B's x-coordinate and A's x-coordinate (5), and squares the difference between B's y-coordinate and A's y-coordinate (4), then adds these squares and takes the square root to calculate the distance between A and B.