point a (4,2) is translated according to the rule (x,y)->(x+1,y-5) then reflected across the y axis
a) what coordinate plane is point a located?
b) what are the coordinates of translated point a?
c) what are the coordinates of reflected point a?
a) Point A is located in the Cartesian plane.
b) The translated point A would be (5, -3). We add 1 to the x-coordinate and subtract 5 from the y-coordinate.
c) Reflecting across the y-axis negates the x-coordinate of the point. Therefore, the reflected point A would be (-5, -3).
Is this correct?
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What does "Cartesian plane" mean?
The Cartesian plane is a 2D coordinate system which consists of two perpendicular number lines, known as the x-axis and y-axis. It provides a way to locate any point in space using two coordinates, typically represented by (x, y) where x represents the horizontal axis and y represents the vertical axis. It is named after the French mathematician and philosopher, René Descartes, who developed the concept of analytical geometry.
Thank you
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yes MLASSAPPE its correct
I'm glad to hear that! If you have any further questions, don't hesitate to ask.
To answer these questions, we will perform the operations step by step.
a) What coordinate plane is point A located?
The coordinate plane consists of two perpendicular number lines called axes: the horizontal x-axis and the vertical y-axis. The point A (4,2) is represented by the x-coordinate (4) and the y-coordinate (2). This means point A is located in the x-y plane.
b) What are the coordinates of the translated point A?
To translate point A, we apply the given rule (x, y) → (x + 1, y - 5).
By substituting the coordinates of point A into the rule, we get:
Translated x-coordinate = 4 + 1 = 5
Translated y-coordinate = 2 - 5 = -3
Therefore, the translated point A is located at (5, -3).
c) What are the coordinates of the reflected point A?
To reflect a point across the y-axis, we need to change the sign of its x-coordinate and keep the y-coordinate the same.
By reflecting point A across the y-axis, we get:
Reflected x-coordinate = -5 (negative of the x-coordinate of the translated point)
Reflected y-coordinate = -3 (same as the y-coordinate of the translated point)
Therefore, the reflected point A is located at (-5, -3).