The diagonal EG of rectangle EFGH has end points of (-2,2) and (3,10). If EF is parallel to the y-axis, what is the perimeter of EFGH?
Make a sketch.
I should be easy to see that GH = 5 and FG = 8
perimeter = 2(5) + 2(8) = 26
To find the perimeter of rectangle EFGH, we need to determine the lengths of all four sides.
Since EF is parallel to the y-axis, it means that the line segment EG is perpendicular to it. Therefore, EG is the height of the rectangle, and its length can be found using the vertical distance between its two endpoints: (-2,2) and (3,10).
The vertical distance between two points can be calculated by subtracting their y-coordinates. In this case, the difference is 10 - 2 = 8.
Now, we know that EG is the height of the rectangle and its length is 8 units.
Since EF is parallel to the y-axis, it means that the line segment FH is perpendicular to it. Therefore, FH is the width of the rectangle, and its length can be found using the horizontal distance between its two endpoints: (-2,2) and (3,2).
The horizontal distance between two points can be calculated by subtracting their x-coordinates. In this case, the difference is 3 - (-2) = 5.
Now, we know that FH is the width of the rectangle and its length is 5 units.
Since opposite sides of a rectangle are equal in length, we can conclude that EF (or HG) is also 8 units, and GH (or FE) is 5 units.
Now we can calculate the perimeter of EFGH by adding up the lengths of all four sides:
Perimeter = EG + GH + HF + FE
= 8 + 5 + 5 + 8
= 26
Therefore, the perimeter of rectangle EFGH is 26 units.