1.

Mathematics

1 answer:

Yanka [14]3 years ago

7 0

Answer:

6 units down

Step-by-step explanation:

Transformation is the movement of a point from its original position to a new position. If an object is transformed, all the point making the object is also transformed. There are four different transformations: Reflection, dilation, translation and rotation.

If y = f(x), y = f(x) + k is a translation k units up if k > 0 and is a translation k units down if k < 0

Given that the parent function is an absolute value represented by:

y = |x|

Therefore comparing y = |xl - 6 with y = f(x) + k, k < 0, therefore this is a translation of 6 units down

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In the figure, and bisect each other. Complete the statements to prove that quadrilateral ABCD is a parallelogram.

Alisiya [41]

Observe the figure below.

Statement Reason

1. AC and BD bisect each other Given

2. AE = EC and BE = ED Definition of bisection

3. $m \angle AEB = m \angle CED$ Vertical angle theorem

Vertical angle theorem states " When two lines intersect each other, the vertically opposite angles are always equal".

4. $\Delta ABE \cong \Delta CDE$ SAS criterion for congruence

5. $m \angle ACD = m \angle CAB$ Corresponding angles of congruent triangles are congruent

6. $AB \parallel CD$ Converse of alternate interior angle theorem

7. $m \angle BEC = m \angle AED$ Vertical angle theorem

8. $\Delta BEC \cong \Delta DEA$ SAS criterion for congruence

9. $BC \parallel AD$ Converse of alternate interior angle theorem

As, $\Delta BEC \cong \Delta DEA$ , so $m \angle CBD = m \angle BDA$ as corresponding parts of corresponding triangles are equal. As these angles are alternate interior angles, so the lines BC and AD are parallel by "Converse of alternate interior angle theorem".