A triangle has vertices of (−3, 3), (−3, 2), and (1, −2). What are the coordinates after dilating from the origin by a scale factor of 1 2 ?

(-1.5, 1.5), '(-1.5, 1) and (0.5, -1)

Step-by-step explanation:

Given the coordinate (x, y) If dilated by a factor k, the resulting coordinate will be (kx, ky).

Similarly given the coordinates of a triangle  (−3, 3), (−3, 2), and (1, −2)

when dilated by a factor of 1/2, the new coordinates will be at;

A (-3, 3) = A'(1/2*-3, 1/2 * 3) = A'(-1.5, 1.5)

B (-3, 2) = B'(1/2*-3, 1/2 * 2) = B'(-1.5, 1)

C (1, -2) = C'(1/2*1, 1/2 * -2) = C'(0.5, -1)

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°

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