Question

1. Find the coordinates of the midpoint of AB for A(5, 12) and B(-4, 8).

2. Find the coordinates of G if P (-5,10) is the midpoint of EG and E has coordinates (-8,6).

Answer 1

1)  The midpoint of AB for A(5, 12) and B(-4, 8) is (1/2, 10)

2) The coordinate of G will be at (-2, -20) if P (-5,10) is the midpoint of EG and E has coordinates (-8,6).

The midpoint of a line is the point that divides such a line into two equal parts.

The formula for calculating the midpoint of a line is expressed as:

$M(X, Y) =(\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )$

1) Given the coordinates A(5, 12) and B(-4, 8).

X = (5+(-4))/2

X = (5-4)/2

X = 1/2

Get the coordinate Y

Y = (12+8)/2

Y = 20/2

Y = 10

Hence the coordinate of the midpoint of AB for A(5, 12) and B(-4, 8) is

(1/2, 10)

The formula for calculating the midpoint of a line is expressed as:

$M(X, Y) =(\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )$

1) Given the midpoint P (-5, 10) and the coordinate  (-8, 6)

Get the X coordinate of G

X = (x1+x2)/2

-5 = (x1-8)/2

-10 = x1 - 8

x1 = -10 + 8

x1 = -2

Get the Y coordinate of G

Y = (y1+y2)/2

10 = (y1+8)/2

20 = y1+8

y1 = 20-8

y1 = 12

Hence the coordinate of G will be at (-2, -20)

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