b In order to find the coordinates of a point S, recall that the slopes of parallel lines are equal.
C
c In order to find the coordinates of a point S, recall that the slopes of parallel lines are equal.
A
aGraph:
B
bCoordinates of the Point S: (6,1)
Quadrilateral:
C
cCoordinates of the Point S: (8,7)
Quadrilateral:
Practice makes perfect
a We have the following points.
P(2,2), Q(7,4), R(3,5)
Let's plot them on the same coordinate plane.
b In order to find the coordinates of a point S, we will follow the following steps.
We will connect the points P and R to have PR and R and Q to have RQ.
We will draw two lines to have quadrilateral PQRS where the opposite sides are parallel. First line will be parallel to PR and pass through the point Q(7,4). The second one will be parallel to RQ and pass through the point P(2,2).
We will identify the point of intersection of the lines and label it S.
Let's start with connecting the points from the previous part.
Next, we will determine the slope of PR to draw a parallel line. To do that we will use the Slope Formula.
m=rise/run=y_2- y_1/x_2- x_1
In the formula, ( x_1, y_1) and ( x_2, y_2) represent the endpoints of the segments.
Thus, the slope of the line which is parallel to PR is 3. Let's use the slope to find a second point and draw the line passes through the point Q(7,4).
The slope of the line which is parallel to RQ is - 14. Let's draw the second line.
Finally, we will identify the point of intersection of the lines and draw the quadrilateral.
As we can see, the coordinates of the point S are (6,1).
c This time, we will find a different point S. To do that we will follow the similar steps as we did in Part B.
We will connect the points P and R to have PR and P and Q to have PQ.
We will draw two lines to have quadrilateral PQRS where the opposite sides are parallel. First line will be parallel to PR and pass through the point Q(7,4). The second one will be parallel to PQ and pass through the point R(3,5).
We will identify the point of intersection of the lines and label it S.
Let's start with connecting the points from the previous part.
Next, we will determine the slope of PR to draw a parallel line to it.
Thus, the slope of the line which is parallel to PR is 3. Let's use the slope to find a second point and draw the line passes through the point Q(7,4).
