Final answer:
To find 1/4 of the distance between points H and T, calculate the full distance using the distance formula and then divide by 4. The calculated distance is 10 units, thus 1/4 of that distance is 2.5 units. However, since this precise value is not an option, the closest answer is 3 units.
Step-by-step explanation:
The question asks, what is 1/4 of the distance between points H (3, -8) and T(-5,-2)? To find the distance between two points in a coordinate plane, we use the distance formula which is derived from the Pythagorean theorem: distance = √((x2 - x1)² + (y2 - y1)²). Points H and T have coordinates (3, -8) and (-5, -2), respectively.
First, subtract the x-coordinates and y-coordinates of H and T to find the differences: Δx = -5 - 3 = -8 and Δy = -2 - (-8) = 6.
Next, square the differences: Δx² = (-8)² = 64 and Δy² = 6² = 36.
Now, sum the squares and take the square root to find the distance: √(64 + 36) = √100 = 10 units.
To find 1/4 of the distance, divide the distance by 4: 10 units / 4 = 2.5 units. There is no option for 2.5 units, so it seems there could be a typo in the provided options. The correct answer to the closest given option would be (b) 3 units, but with the note that it should be 2.5 units if precise calculation is considered.