Assume that the lines DE and XY intersect as in the diagram below. which of the following statements are true
2 answers:
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System 1: The solution is (x, y) = (-4, 5)
System 2: The solution is
<em><u>Solution:</u></em>
<em><u>Given system of equations are:</u></em>
2x + 3y = 7 ------ eqn 1
-3x - 5y = -13 --------- eqn 2
We can solve by elimination method
Multiply eqn 1 by 3
6x + 9y = 21 ------ eqn 3
Multiply eqn 2 by 2
-6x - 10y = -26 ------- eqn 4
Add eqn 3 and eqn 4
6x + 9y -6x - 10y = 21 - 26
-y = -5
y = 5
Substitute y = 5 in eqn 1
2x + 3(5) = 7
2x + 15 = 7
2x = -8
x = -4
Thus the solution is (x, y) = (-4, 5)
<h3><em><u>Second system of equation is:</u></em></h3>8 - y = 3x ------ eqn 1
2y + 3x = 5 ----- eqn 2
We can solve by susbtitution method
From given,
y = 8 - 3x ----- eqn 3
Substitute eqn 3 in eqn 2
2(8 - 3x) + 3x = 5
16 - 6x + 3x = 5
3x = 16 - 5
3x = 11
Substitute the above value of x in eqn 3
y = 8 - 3x
Thus the solution is
Answer: The correct option is second, a rotation clockwise about the origin followed by a reflection across the x-axis.
Explanation:
From the given figure it is noticed that the vertices of ΔABC are A(-6,4), B(-4,6), C(-2,2) and vertices of ΔA'B'C' are A'(4,-6), B(6,-4), C(2,-2).
It means if the point is P(x,y) then after transformation it will be P'(y,x).
If a point P(x,y) reflection across the y-axis followed by a reflection across the x-axis, then the image of point after transformation will be P'(-x,-y), therefore it is not the correct option.
If a shape is rotated clockwise about the origin then the point P(x,y) will be P'(y,-x) and after that reflect across the x-axis, so the point after transformation will be P'(y,x), therefore it is the correct option.
If a shape is rotated clockwise about the origin then the point P(x,y) will be P'(-y,x) and after that reflect across the x-axis, so the point after transformation will be P'(-y,-x), therefore it is not the correct option.
If a point P(x,y) reflection across the x-axis followed by a reflection across the y-axis, then the image of point after transformation will be P'(-x,-y), therefore it is not the correct option.
Hence, the correct option is second, a rotation clockwise about the origin followed by a reflection across the x-axis.