Math  /  Geometry

Questioncorresponding side length of quadina
2 A triangle will be dilated on the coordinate grid to create a larger triangle. The triangle is dilated using the origin as the center of dilation. Write a rule that could represent this dilation. Write the correct answer in each box. Not all answers will be used. 0.25x0.25 x \square 4x4 x \square x1.5x-1.5 \square \square y+1.5y+1.5
The triangle was dilated according to the rule (x,y)((x, y) \rightarrow( \square \square ) e2024 登

Studdy Solution

STEP 1

What is this asking? We need to pick the rule that makes a triangle bigger when it's blown up from the origin! Watch out! Don't mix up shrinking and growing!
We want a bigger triangle, not a smaller one.

STEP 2

1. Understand Dilation
2. Choose the Right Rule

STEP 3

Dilation is like blowing up a balloon!
Everything gets bigger or smaller from a center point.
Here, the center point is the **origin** (0,0)(0,0).

STEP 4

We multiply the *x* and *y* coordinates by a **scale factor**.
If the scale factor is *greater* than 1, the shape gets bigger.
If it's *between* 0 and 1, it gets smaller.

STEP 5

We have 0.25x0.25x, 4x4x, x1.5x - 1.5, 0.25y0.25y, 4y4y, and y+1.5y + 1.5.
We need to multiply, not add or subtract, to dilate.

STEP 6

0.250.25 is the same as 14\frac{1}{4}, which would make the triangle *smaller*.
We want *bigger*, so we need a scale factor *greater* than 1.
That means 44 is our winner!

STEP 7

We multiply *both* the *x* and *y* coordinates by our **scale factor** of 44.
So, our rule is (x,y)(4x,4y)(x, y) \rightarrow (4 \cdot x, 4 \cdot y), or more simply, (x,y)(4x,4y)(x, y) \rightarrow (4x, 4y).

STEP 8

The rule that represents this dilation is (x,y)(4x,4y)(x, y) \rightarrow (4x, 4y).
We put 4x4x in the first box and 4y4y in the second box.

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord