Question

If p(4,2a+1) is the midpoint of the line segment joining the points (a-1,3) and (5,b+7), find the coordinates of the point P.​

Answer 1

Answer:

p(4,9)

Step-by-step explanation:

Okay so the point p(4,2a+1) is the midpoint of the line segment joining the points (a-1,3) and (5,b+7).

Now we know that the coordinates of a midpoint of a line are determined using the following formula,

let x and y be the corresponding coordinates, then:

$x = \frac{5 + (a - 1)}{2}$

$y = \frac{(b+7) + 3}{2}$

Now we have the value of x

$4 = \frac{5 + a - 1}{2} \\ 4 = \frac{4 + a}{2} \\ 8 = 4 + a \\ a = 8 - 4\\ a = 4$

Now putting the value of a into given coordinate for y

$y = (2(4) + 1) \\ y = 8+1 \\ y = 9$

Hence, we have the coordinates p(4,9)