Question

under a dilation, the point (2,6) is moved to (6,18) what is the scale factor of the dilation? enter your answer in the box​

Answer 1

Answer:3

Explanation:

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Answer 2

3

Explanation:

The equation of line passing through the two points is
`(y-y_(1) )/(x-x_(1) )=(y_(2) -y_(1))/(x_(2) -x_(1))`

When substituted,the equation becomes
`(y-6)/(x-2)=(18-6)/(6-2)`

which when simplified is
`y=3* x`

The line clearly passes through origin.

The distance between two points is
`\sqrt{(y_(1)-y_(2) )^(2)+(x_(1)- x_(2) )^(2)}`

Distance between origin and
`(2,6)` is
`√(40)`.

Distance between origin and
`(6,18)` is
`√(360)`

Scale factor is
`\frac{distance\text{ }of\text{ }p_(2)\text{ from origin}}{distance \text{ } of \text{ } p_(1)\text{ from origin}}`

So,scale factor is
`(√(360) )/(√(40) )`

which when simplified becomes 3.