Final answer:
To find the distance between two points using the distance formula, plug the coordinates into the formula and simplify the expression. For part (a), the distance between Point T(2,3) and Point W(-7,-5) is approximately 12.04 units. For part (b), the length of FG is approximately 17.46 units.
Step-by-step explanation:
a) To find the distance between two points using the distance formula, we need to know the coordinates of the two points. Let's call the coordinates of Point T (x1, y1) and the coordinates of Point W (x2, y2). The distance formula is given by:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Plugging in the coordinates, we get:
d = sqrt((-7 - 2)^2 + (-5 - 3)^2)
= sqrt((-9)^2 + (-8)^2)
= sqrt(81 + 64)
= sqrt(145)
≈ 12.04
Therefore, the distance between Point T(2,3) and Point W(-7,-5) is approximately 12.04 units.
b) Let's consider the coordinates of Point F (x1, y1) as (7, -2) and the coordinates of Point G (x2, y2) as (-9, 5). Using the distance formula, we have:
d = sqrt((-9 - 7)^2 + (5 - (-2))^2)
= sqrt((-16)^2 + (7)^2)
= sqrt(256 + 49)
= sqrt(305)
≈ 17.46
Therefore, the length of FG is approximately 17.46 units.