If center of dilation is D (-1, -1) and the coordinates for triangle ABC are A(0, -2), B(2, -4), and C(3, -1), then what are the coordinates of triangle A'B'C' after a dilation with a scale factor of 2?

A'(1,-3), B'(7,-1) and C'(5,-7).

Step-by-step explanation:

Given,

The coordinates of the triangle ABC are,

A(0, -2), B(2, -4), and C(3, -1)

If a point (x,y) is dilated about a point (p,q) with a scale factor k,

Then the dilation rule is,

Here, the triangle ABC with coordinates A(0, -2), B(2, -4), and C(3, -1) is dilated with scale factor 2 about a point (-1,-1) to form triangle A'B'C'.

That is, k = 2, p = -1, q = -1

Then,

Similarly,

Therefore, the coordinates of triangle A'B'C' are,

A'(1,-3), B'(5,-7) and C'(7,-1)

answer: yes youre right.

step-by-step explanation:

option a, c,d are correct.

step-by-step explanation:

from the given figure, it is given that z is equidistant from the sides of the triangle rst, then from triangle tzb and triangle szb, we have

tz=sz(given)

bz=zb(common)

therefore, by rhs rule,δtzb ≅δszb

by cpctc, sz≅tz

also, from δctz and δasz,

tz=sz(given)

∠tcz=∠saz(90°)

by rhs rule, δctz ≅ δasz, therefore by cpctc, ∠ctz≅∠asz

also,from δasz and δzsb,

zs=sz(common)

∠zbs=∠saz=90°

by rhs rule, δasz ≅δzsb, therefore, by cpctc, ∠asz≅∠zsb

hence, option a, c,d are correct.