Math / Geometry

QuestionDraw the following quadrilateral after a translation 1 unit to the left and 4 units $u$

Studdy Solution

STEP 1

What is this asking? We need to shift a quadrilateral on a graph 1 unit to the left and 4 units up! Watch out! Don't mix up left and right, or up and down!
Also, make sure to move every corner of the shape.

STEP 2

1. Find Initial Coordinates
2. Shift the Coordinates
3. Draw the New Quadrilateral

STEP 3

Let's locate those starting points!
We've got four corners to our quadrilateral.
Looking closely, we can see the coordinates are approximately $(2, 4)$ , $(3, 2)$ , $(1, -2)$ , and $(-2, 1)$ .

STEP 4

Time to slide that shape!
Moving 1 unit to the left means we subtract $1$ from each $x$ -coordinate.
Moving 4 units up means we add $4$ to each $y$ -coordinate.

STEP 5

Let's transform the first point, $(2, 4)$ .
Subtracting $1$ from the $x$ -coordinate gives us $2 - 1 = 1$ .
Adding $4$ to the $y$ -coordinate gives us $4 + 4 = 8$ .
So, our new point is $(1, 8)$ !

STEP 6

Now for $(3, 2)$ . $3 - 1 = 2$ and $2 + 4 = 6$ , giving us $(2, 6)$ .

STEP 7

Next, $(1, -2)$ becomes $(1 - 1, -2 + 4) = (0, 2)$ .

STEP 8

Finally, $(-2, 1)$ transforms to $(-2 - 1, 1 + 4) = (-3, 5)$ .

STEP 9

Plot those new points: $(1, 8)$ , $(2, 6)$ , $(0, 2)$ , and $(-3, 5)$ on the graph.
Then, connect the dots to draw your translated quadrilateral!

STEP 10

The translated quadrilateral has vertices at $(1, 8)$ , $(2, 6)$ , $(0, 2)$ , and $(-3, 5)$ .
Draw these points on a graph and connect them to form the new quadrilateral.

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