Triangles and are shown on the coordinate plane below.
The slope of A-C is at point B. A-B is parallel to x-axis and C-B is parallel to y-axis and slope of D-F is at point E. D-E is parallel to x- axis and F-E is parallel to y-axis. The slope of line A-F is at point P and A-P is parallel to x-axis and F-P is parallel to y-axis.
Which statement explains why the slope of
is equal to the slope of
?
A.
The ratio of to is equal to the ratio of to .
B.
The ratio of to is equal to the ratio of to .
C.
The ratio of to is equal to the ratio of to .
D.
The ratio of to is equal to the ratio of to .
B. The ratio of AB to DF is equal to the ratio of BC to EF.
The correct statement that explains why the slope of line AB is equal to the slope of line AF is:
A. The ratio of AB to AC is equal to the ratio of AF to AP.
To determine why the slope of ΔABC is equal to the slope of ΔDEF, we need to analyze the given information about the slopes and orientations of the line segments in the triangles.
From the information provided, we know that the line segment AB is parallel to the x-axis, and line segment CB is parallel to the y-axis. This means that the slope of AB is 0 (since it is a horizontal line), and the slope of CB is undefined (since it is a vertical line).
Similarly, we know that the line segment DE is parallel to the x-axis, and line segment FE is parallel to the y-axis. Therefore, the slope of DE is also 0, and the slope of FE is undefined.
Now, let's look at the line segment AF, which connects the vertices A and F of the triangles. To find its slope, we can analyze its orientation. We can see that line segment AP is parallel to the x-axis (horizontal), and line segment FP is parallel to the y-axis (vertical).
Based on this information, we can conclude that the slope of AF will be the same as the slopes of AB and CB since AB is parallel to AP, and CB is parallel to FP.
Therefore, the correct statement that explains why the slope of ΔABC is equal to the slope of ΔDEF is:
B. The ratio of AB to CB is equal to the ratio of AP to FP.