This might not resemble a familiar figure at first sight. However, by calculating the slope of WZ and XY, we see that they are the same.
m_(wz)&=6-7/5-3 ⇒ m_(wz)= - 1/2 [0.8em]
m_(xy)&=1-4/9-3 ⇒ m_(xy)=- 1/2
Since this is a quadrilateral with a pair of parallel sides, this is a trapezoid.
b
To calculate the perimeter, we have to find all of its sides. The side WX, is the vertical distance between the segment's endpoints.
To find the values of the remaining sides, we have to use the Distance Formula.
Segment
Points
sqrt((x_2-x_1)^2+(y_2-y_1)^2)
d
XY
( 3,4), ( 9,1)
sqrt(( 3- 9)^2+( 4- 1)^2)
sqrt(45)
WZ
( 5,6), ( 3,7)
sqrt(( 5- 3)^2+( 6- 7)^2)
sqrt(5)
ZY
( 9,1), ( 5,6)
sqrt(( 9- 5)^2+( 1- 6)^2)
sqrt(41)
When we know the length of all sides, we can find the perimeter.
c
Examining the transformation, we see that the x-coordinates change signs while the y-coordinates are unchanged. This corresponds to a reflection in the y-axis. Let's perform this reflection on Y.
To rotate a point by 90^(∘) clockwise about the origin, we draw segments from it to the origin. Next, we use a protractor to draw a second segment that is at a 90^(∘) angle clockwise to the first segment. To find the coordinates of the rotated point, we have to make the second segment the same length as the first. Let's demonstrate with one of the points.
If we repeat the procedure for the remaining three points, we can draw the rotated trapezoid.
To find the slope of W''Z'', we could use the Slope Formula. However, in Part A we calculated the slope of WZ to be - 12. When rotating the trapezoid 90^(∘), the slope of W''Z'' and WZ will be negative reciprocals.
m_1 m_2=- 1
By substituting the slope of WZ, in this formula, we can calculate the perpendicular slope.
