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Mathematics

2 answers:

Alchen [17]3 years ago

8 0

Answer:

$\bar{AD}\parallel \bar{BC}$

Step-by-step explanation:

If $m\angle 4=m\angle8$ , then $m\angle4$ and $m\angle4$ are alternate interior angles.

This means that line segment AC is a transversal.

This implies that line segment AD is parallel to line segment BC.

The second choice is the correct answer.

Vera_Pavlovna [14]3 years ago

4 0

Answer:

The correct answer is second option.

AD ║ BC

Step-by-step explanation:

Alternate interior angles in a parallel lines are equal.

From the figure we can see quadrilateral ABCD.

It is given that m<8 = m<4

Consider the line segment AD and BC,and AC is a traversal on these lines, m<8 and m<4 are alternate interior angles, which is equal.From this we can conclude that, AD║ BC

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What is the scale factor in the dilation if the coordinates of A prime are (–7, 6) and the coordinates of C prime are (–4, 3)?

olchik [2.2K]

Option A: $\frac{1}{3}$ is the dilation factor

Explanation:

The Coordinates of the square ABCD are A(-21,18), B(-12,18), C(-12,9), D(-21,9)

Also, the coordinates of the square A'B'C'D' are A'(–7, 6), B'(-4,6), C'(-4,3), D'(-8,3)

Now, we shall determine the scale factor in the dilation if the coordinates A' and C'.

Since, the dilation is the enlargement of the image in the same shape but different size.

To determine the scale factor, let us divide A'C' by AC

Thus, we have,

$\begin{aligned}A^{\prime} C^{\prime} &=\sqrt{(-4+7)^{2}+(3-6)^{2}} \\&=\sqrt{3^{2}+(-3)^{2}} \\&=\sqrt{9+9} \\&=\sqrt{18}\\&=3\sqrt{2} \end{aligned}$