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In the coordinate plane, point B has coordinates (2,3) and is the midpoint of the line segment AC. The coordinates of points A and C are (p,7) and (−6,−1), respectively. What is the value of p ?

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Answer:

The value of p is 10

Step-by-step explanation:

Here, we are told that the midpoint of the segment AC is B. What this means is that, applying the midpoint formula on AC would give the coordinates of B.

Mathematically;

(x,y) = {(x1 + x2)/2, (y1 + y2)/2}

(2,3) = (p -6)/2 , (7-1)/2

equating identities;

(p-6)/2 = 2

p-6 = 2 * 2

p-6 = 4

p = 4 + 6

p = 10

adioabiola

The value of p as described in the question is; 10

Since the point B, with coordinates (2,3) is the midpoint of the line segment AC.

Therefore, the x-coordinate of point B (2) is the midpoint of the x-coordinate of point A and C.

The value of p can then be evaluated as follows;

  • (p + (-6))/2 = 2

By Cross-product; we have;

  • p - 6 = 4

  • p = 4 + 6

  • p = 10.

The value of p is therefore; 10

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