Final answer:
The calculated distance from the point (15, -21) to the given line using the point-to-line distance formula is approximately 21.0 units, which does not match the provided multiple-choice options.
Step-by-step explanation:
To find the distance from the point (15, -21) to the line 5x - 2y = 4, we can use the point-to-line distance formula:
Distance = |Ax1 + By1 + C| / √(A² + B²)
Where (x1, y1) is the point (15, -21), and A, B, and C are from the line equation 5x - 2y = 4 rewritten in standard form Ax + By + C = 0, which is 5x - 2y - 4 = 0. In this case, A = 5, B = -2, and C = -4.
Plugging in the values, we get:
Distance = |(5)(15) + (-2)(-21) - 4| / √(5² + (-2)²)
= |75 + 42 - 4| / √(25 + 4)
= |113| / √29
= 113 / √29
Rounding to the nearest tenth, the distance is approximately 21.0 units.
However, this answer is not among the options provided (a) 7.8, (b) 9.2, (c) 11.4, (d) 13.7, which suggests there may be an error in the calculation or in the options listed. It is important to double-check calculations and ensure that the formula has been applied correctly.