Answer:
(x, y) = (2, 9)
Step-by-step explanation:
For the triangles to be congruent, the hypotenuses must be the same length:
y = x + 7
and the marked leg must be the same length in each triangle:
y -3 = 4x -2
These are two equations in two unknowns (a "system" of equations) that can be solved in any of the usual ways. Since the first equation gives an expression for y, it is convenient to substitute that into the second equation:
(x +7) -3 = 4x -2
x +4 = 4x -2 . . . . . . collect terms
x +6 = 4x . . . . . . . . .add 2
6 = 3x . . . . . . . . . . . subtract x
2 = x . . . . . . . . . . . . divide by 3
y = 2 + 7 = 9 . . . . . .substitute for x in the first equation
The values you're looking for are x = 2, y = 9.
Answer:
Isosceles Acute Triangle
Step-by-step explanation:
Isosceles=2 sides that are equal (I saw 2)
Acute=3 acute angles (3<90)
E (3.75,-2.5)
G(-0.75, -3)
Point E is the midpoint of the segment AB, then it has coordinates:
(-3+6/2, -1+(-3)/2)= (3/2,-2)
Point F is the midpoint of the segment EB, then it has coordinates:
(3/2+6/2, -2+(-3)/2)= (15/4,5/2)= (3.75, -25)
Let S be the midpoint of segment CB, then it has coordinates:
(-3+6/2,-3+(-3)/2)= (3/2,-3)
Point G is the midpoint of segment CS, then its coordinates are:
(3/2+6/2, -3+(-3)/2)=(-3/4,-3)= (-0.75,-3)
Hope this helps!