The coordinates of the endpoints of AB are A(−4, 3) and B(1, −3). Which measurement is closest to the length of AB in units?
Responses
A 8.4 units8.4 units
B 6.8 units6.8 units
C 7.4 units7.4 units
D 7.8 units7.8 units
The distance formula is \(\sqrt{(x2-x1)^2 + (y2-y1)^2}\).
Using the coordinates of A (-4, 3) and B (1, -3), we get:
\(\sqrt{(1-(-4))^2 + (-3-3)^2} = \sqrt{5^2 + (-6)^2} = \sqrt{25 + 36} = \sqrt{61}\)
Approximating \(\sqrt{61}\):
\(\sqrt{61} \approx 7.8\)
Therefore, the closest measurement to the length of AB in units is 7.8 units. Choice D.