the right arrow symbol used to the transition from a point to its image after a transformation is not contained within the equation editor. if such a symbol is needed, type "right arrow". for example: p (0,0) right arrow p(1,2).
triangle ABC has coordinates A(1,4); B(3,-2); and C(4,2). find the coordinates of the image A'B'C after a reflection over the x-axis.
help me I don't understand a single word of this!
reflection over the x-axis: the x stays the same, the y changes signs
or
(x,y) ------> (x, -y)
A(1,4) ----> A' (1,-4)
B(3,-2) ----> ......
you do the others
Don't worry, I'm here to help you step-by-step!
To find the image of triangle ABC after a reflection over the x-axis, we need to reflect each of the vertices of the triangle.
Step 1: Reflect point A(1,4) over the x-axis:
When we reflect a point over the x-axis, the y-coordinate changes sign. So, the image of point A will have the same x-coordinate but a negated y-coordinate. The new coordinates will be (1, -4).
Step 2: Reflect point B(3,-2) over the x-axis:
Again, when we reflect a point over the x-axis, the y-coordinate changes sign. So, the image of point B will have the same x-coordinate but a negated y-coordinate. The new coordinates will be (3, 2).
Step 3: Reflect point C(4,2) over the x-axis:
Similarly, when we reflect a point over the x-axis, the y-coordinate changes sign. So, the image of point C will have the same x-coordinate but a negated y-coordinate. The new coordinates will be (4, -2).
So, the coordinates of the image triangle A'B'C after a reflection over the x-axis are:
A'(1, -4)
B'(3, 2)
C'(4, -2)
I hope this helps! Let me know if you have any further questions.