Triangles HJK and PMK are similar right triangles. The coordinates of all the vertices are integers.

Question

Which statement is true of the slope of HK and PK ?
Responses
A The slope of HK is less than the slope of PK , because the ratio of the change in y-values of the endpoints to the change in x-values of the endpoints is less for HK than it is for PK.The slope of HK is less than the slope of PK , because the ratio of the change in y-values of the endpoints to the change in x-values of the endpoints is less for HK than it is for PK.
B The slope of HK is greater than the slope of PK , because the ratio of the change in y-values of the endpoints to the change in x-values of the endpoints is greater for HK than it is for PK.The slope of HK is greater than the slope of PK , because the ratio of the change in y-values of the endpoints to the change in x-values of the endpoints is greater for HK than it is for PK.
C The slope of HK is equal to the slope of PK , because the ratio of the change in y-values of the endpoints to the change in x-values of the endpoints is the same for HK as it is for PK.The slope of HK is equal to the slope of PK , because the ratio of the change in y-values of the endpoints to the change in x-values of the endpoints is the same for HK as it is for PK.
D The relationship between the slope of HK and the slope of PK cannot be determined, because the triangles are congruent.The relationship between the slope of HK and the slope of PK cannot be determined, because the triangles are congruent.

Answer 1

C The slope of HK is equal to the slope of PK, because the ratio of the change in y-values of the endpoints to the change in x-values of the endpoints is the same for HK as it is for PK. Since the triangles are similar, corresponding sides are in proportion and therefore the slopes of the corresponding sides will be the same.