Final answer:
The value of 'a' is -4, as it is calculated using the midpoint formula applied to the x-coordinates of the endpoints A and B, which yields the result that point P is indeed the midpoint of the line segment joining A and B. Therefore, the value of 'a' is -4. So the answer is (A) -4.
Step-by-step explanation:
The student has asked to find the value of 'a' given that point P(a/8,4) is the midpoint of the line segment joining points A(-5, 2) and B(4, 6). To find the value of 'a', we use the midpoint formula for a line segment, which is M = ((x1 + x2)/2, (y1 + y2)/2), where M is the midpoint, and (x1, y1) and (x2, y2) are the coordinates of the endpoints A and B, respectively.
For the x-coordinates, we have (-5 + 4)/2 = a/8. Simplifying, we get -1/2 = a/8. Multiplying both sides of the equation by 8 gives us -4 = a, which means the value of 'a' is -4.
For the y-coordinates, we have (2 + 6)/2 = 4. This is true since 8/2 equals 4, which confirms that the y-coordinate of the midpoint P is correctly given as 4.
To find the value of 'a', we can use the midpoint formula.
The midpoint formula states that the coordinates of the midpoint of a line segment between two points (x1, y1) and (x2, y2) is given by the formula ((x1 + x2)/2, (y1 + y2)/2). In this case, the coordinates of the midpoint P(a/8, 4) are equal to the average of the x-coordinates and the average of the y-coordinates of points A(-5, 2) and B(4, 6).
Using the midpoint formula, we can set up the following equations:
a/8 = (-5 + 4)/2
4 = (2 + 6)/2
Simplifying these equations, we get:
a/8 = -1/2
4 = 8/2
Multiplying both sides of the first equation by 8 to eliminate the fraction, we get:
a = -4
Therefore, the value of 'a' is -4. So the answer is (A) -4.