To find the coordinate of the point D, we can use the
Midpoint point of a line Segment formula. Calculation of the formula are as
follows,
Given two points A(x1,y1) and C(x2,y2), we need to locate
the midpoint coordinate of this line denoted as B(x,y).
To solve for the value of x and y, we get,
x=(x1+x2)/2 and y=(y1+y2)/2
For the given problem, we need to solve first the midpoint
coordinate of AC which is B.
So, A(-9,-4)=A(x1,y1) and C(-1,6)=C(x2,y2)
Hence,
B(x,y)=B((-9+(-1))/2, (-4+6)/2)=B(-10/2,2/2)=B(-5,1)
Now, since the midpoint is given but one point in the line
is missing. To solve for the missing point D(x2,y2), we need to use the
Midpoint Segment Formula.
That is, B(-5,1)=B(x,y)
and E(-4,-3)=E(x1,y1)
So,
x=(x1+x2)/2 and y=(y1+y2)/2
-5=(-4+x2)/2 and 1=(-3+y2)/2
By Cross Multiplication and Transposing method,
-5(2)=-4+x2 and 1(2)=-3+y2
x2=-10+4=-6 and y2=3+2=5
Thus, the coordinate of D is D(-6,5).
