Answer:
Coordinates of fourth vertex are (8,9)
Step-by-step explanation:
Given that Laura is designing a rectangular porch for her house. On her scale drawing, the vertices of the rectangle are (2, 7), (8, 7), and (2, 9).
we have to find the coordinates of the fourth vertex.
As diagonals of rectangle bisect each other and are congruent then the coordinates of E is the mid-point of AC as well as BD.
By mid-point formula if (a,b) and (c,d) are the coordinates of line segment then the coordinates of mid point are
\((\frac{a+c}{2},\frac{b+d}{2})\)
Mid-point of AC= mid point of BD
\((\frac{a+2}{2},\frac{b+7}{2})=(\frac{8+2}{2},\frac{7+9}{2})\)
\((\frac{a+2}{2},\frac{b+7}{2})=(5,8)\)
Comparing both sides , we get
\(\frac{a+2}{2}=5\) and \(\frac{b+7}{2}=8\)
\(a+2=10\) and \(b+7=16\)
\(a=8\) and \(b=9\)
Hence, coordinates of fourth vertex are (8,9)
