A triangle with a vertex (−3, 5) is translated up 6 units. What are the coordinates of this vertex after it is translated? Draw a graph if necessary.(1 point)
1) (-3,11)
2) (6,-4)
3) (-8,-2)
4) (-2,8)
5) 6
for the quick check.
1) up or down
2) left or right
3) (6,0)
4) Add 3 units to each x -value and subtract 4 units from each y -value.
5) Subtract 6 units from each x-value and add 5 units to each y-value.
When a point is translated up 6 units, the y-coordinate increases by 6.
So the new coordinates of the vertex after it is translated up 6 units are: (-3, 5+6) = (-3, 11).
Here is a graph showing the original vertex (-3, 5) and the translated vertex (-3, 11):
\begin{xy}
(0,0) *{.};
(-1,-1) *{(-3, 5)};
(-1,-2) *{(-3, 11)};
(0,-3) *{}="A";
(0,-1) *{};
(0,0) *{};
(0,1) *{};
(0,3) *{};
(0,4) *{};
(-3,5); (0,-3) **[blue] @{-};
(-3,5.1); (0,-3.1) **[red] @{-};
\end{xy}
I apologize for the mistake. The correct translation for a vertex (-3, 5) being moved up 6 units is (x, y+6), which would be (-3, 5+6) = (-3, 11).
So the correct coordinates of the translated vertex are (-3, 11).
Here is the updated graph showing the original vertex (-3, 5) and the translated vertex (-3, 11):
\begin{xy}
(0,0) *{.};
(-1,-1) *{(-3, 5)};
(-1,-2) *{(-3, 11)};
(0,-3) *{}="A";
(0,-1) *{};
(0,0) *{};
(0,1) *{};
(0,3) *{};
(0,4) *{};
(-3,5); (0,-3) **[blue] @{-};
(-3,5.1); (0,-2.9) **[red] @{-};
\end{xy}
1) "Up or down" refers to the movement in the y-direction.
2) "Left or right" refers to the movement in the x-direction.
3) (6,0) represents a point that is translated 6 units to the right on the x-axis.
4) "Add 3 units to each x-value and subtract 4 units from each y-value" means that each x-coordinate is increased by 3 units and each y-coordinate is decreased by 4 units.
5) "Subtract 6 units from each x-value and add 5 units to each y-value" means that each x-coordinate is decreased by 6 units and each y-coordinate is increased by 5 units.