Question 1
On the above right triangle perform a dilation of scale factor 
Which of the following correctly shows 
Explanation: The orthocenter of a triangle can be located by finding the intersection of the three altitudes of the triangle - the segments connecting each vertex to its opposite side, perpendicular to the respective side. Since the triangle is right, 
and 
are two of the altitudes, which intersect at 
; the third altitude must also pass through 
, since the three altitudes are concurrent. Therefore, we perform a dilation of the triangle with respect to center 
.
This is done by mapping 
and 
to the midpoints of 
and 
, respectively, and by mapping 
to itself. The triangle is seen below:
This figure is the correct choice.
and 
are two of the altitudes, which intersect at 
; the third altitude must also pass through 
, since the three altitudes are concurrent. Therefore, we perform a dilation of the triangle with respect to center 
.
This is done by mapping 
and 
to the midpoints of 
and 
, respectively, and by mapping 
to itself. The triangle is seen below:
This figure is the correct choice.