Question

re - write the following statement as a conditional (\if - then\) statement.
the longest side of a right triangle is the hypotenuse.
a. if the figure has a hypotenuse, then it is a right triangle.
b. if the figure is a right triangle, then it has exactly one hypotenuse.
c. if the segment is the longest side of a triangle. then it is the hypotenuse.
d. if the segment is the longest side of a right triangle, then it is the hypotenuse.
question 2: current: ma.912.gr.2.1
which transformation rule maps \\( \triangle abc \\) to \\( \triangle a ^ { \prime } b ^ { \prime } c ^ { \prime } \\)
a \\( ( x, y ) \
ightarrow ( x - 5, y + 4 ) \\)
b \\( ( x, y ) \
ightarrow ( x + 5, y - 4 ) \\)
c \\( ( x, y ) \
ightarrow ( x - 4, y + 5 ) \\)
d \\( ( x, y ) \
ightarrow ( x + 4, y - 5 ) \\)

Explanation:

Step1: Find coordinates of points

Let's assume \(A(-8,1)\), \(B(-6,6)\), \(C(-4,1)\) and \(A'(-3,-3)\), \(B'(-1,2)\), \(C'(1,-3)\)

Step2: Calculate the change in \(x\) and \(y\) - coordinates

For point \(A\): \(x\) - coordinate changes from \(-8\) to \(-3\) (\(-3-(-8)=5\)), \(y\) - coordinate changes from \(1\) to \(-3\) (\(-3 - 1=-4\))
For point \(B\): \(x\) - coordinate changes from \(-6\) to \(-1\) (\(-1-(-6)=5\)), \(y\) - coordinate changes from \(6\) to \(2\) (\(2 - 6=-4\))
For point \(C\): \(x\) - coordinate changes from \(-4\) to \(1\) (\(1-(-4)=5\)), \(y\) - coordinate changes from \(1\) to \(-3\) (\(-3 - 1=-4\))

The transformation rule is \((x,y)\to(x + 5,y-4)\)

Answer:

B. \((x,y)\to(x + 5,y-4)\)