point r has coordinates (a,b). the point is reflected across the x axis and then translated 5 points to the right to create point s. Create an expression that represent the y coordinates of point s
(a,b) ---> reflected across the x-axis ---> (a, -b)
(a,-6) ---> translated 5 units to the right ---> (a+5, -b)
To find the y-coordinate of point S, we need to perform two operations on point R: reflection across the x-axis and translation 5 points to the right.
1. Reflection across the x-axis: When we reflect a point across the x-axis, the sign of its y-coordinate changes. So, the y-coordinate of point R after reflection will be -b.
2. Translation 5 points to the right: To translate a point to the right, we add the given value (5 in this case) to its x-coordinate. So, the x-coordinate of point S will be a + 5.
Therefore, the expression that represents the y-coordinate of point S is -b.
To find the y-coordinate of point S after reflecting point R across the x-axis and then translating it 5 units to the right, you can follow these steps:
1. Reflecting across the x-axis: When a point is reflected across the x-axis, the sign of its y-coordinate changes. So, if point R has coordinates (a, b), after reflecting it across the x-axis, the new y-coordinate becomes -b.
2. Translating 5 units to the right: To translate a point horizontally 5 units to the right, you add 5 to its x-coordinate. So, if we reflect point R first, then translate it horizontally, the new x-coordinate becomes (a + 5).
Therefore, the coordinates of point S after both operations are (-a + 5, -b).
To represent the y-coordinate of point S, you can use the expression:
-y-coordinate of S = -b
Or, in simplified form:
y-coordinate of S = b