Question

Help me solve this please

Answer 1

D'G' = 52.5 units

Explanation:

Since the dilatation is centred at the origin then multiply the original coordinates by the scale factor 3.5

D' = (1 × 3.5, 7 × 3.5 ) = (3.5, 24.5 )

G' = (- 8 × 3.5, - 5 × 3.5 ) = (- 28, - 17.5 )

Calculate D'G' using the distance formula

d =
`\sqrt{(x_(2)-x_(1))^2+(y_(2)-y_(1))^2 }`

with (x₁, y₁ ) = D' (3.5, 24.5) and (x₂, y₂ ) = G' (- 28, - 17.5)

D'G' =
`√((-28-3.5)^2+(-17.5-24.5)^2)`

=
`√((-31.5)^2+42^2)`

=
`√(992.25+1764)`

=
`√(2756.25)`

= 52.5 units