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Point P(a/8,4) is the mid-point of the line segment joining the points A(-5, 2) and B(4, 6). The value of 'a' is

(A) – 4

(B) 4

(C) - 8

(D) – 2​

User Wally Ali
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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.

User Dave Barnett
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