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Kitty [74]
3 years ago
12

The pre-image point B(-4, 3) is translated to B'(-1, 1). What was the translation used?

Mathematics
1 answer:
Otrada [13]3 years ago
3 0
<span>(x + 3,y - 2)
</span>
=B'(-1, 1)
x = -4, y = 3
(x,y) 
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What is the image of (2,3)(2,3) after a reflection over the line y=-xy=−x?
saw5 [17]

Answer:

The image of (2,3) after a reflection over the given line will be: (-3,-2)

Step-by-step explanation:

The given point is (2,3)

Let (x,y) be a point, when it will be reflected over the line y=-x the coordinates are exchanged and are negated i.e. point (x,y) becomes (-y,-x)

When a point is reflected over a line the distance between the image of point and the line remains the same as the distance between original point and line.

Given point will become: (-3,-2)

Hence,

The image of (2,3) after a reflection over the given line will be: (-3,-2)

5 0
3 years ago
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Abcdefgh is a regular octagon. M is a point on the line dh. N is a point on the line fm. The line dn and fm are perpendicular. P
Aloiza [94]

ΔFHM and ΔDFP by addition to ΔMOF and ΔPDO respectively gives

ΔHOP and ΔDOF, which are congruent.

Response:

  • ΔFHM ≅ ΔDFP by transitive property of equality

<h3>Methods used to prove that the two triangles are congruent</h3>

Based on the properties of a regular octagon, the diagonals DH and BF

of a regular octagon are perpendicular, and they bisect each other,

given that the length of half the diagonal represent the radius of the

circumscribing circle.

Therefore;

∠NFP ≅ ∠NFP by reflexive property

∠PNF ≅ ∠MOF all right angles are congruent

ΔMOF is similar to ΔPNF by Angle-Angle AA similarity postulate.

∠OMF ≅ ∠DMN by reflexive property

Therefore;

ΔDMN is similar to ΔMOF by AA similarity postulate.

Similarly, we have;

ΔDMN ~ ΔPDO by AA similarity postulate;

Therefore;

ΔPDO is similar to ΔOMF by transitive property

∠ODP ≅ ∠OFM by CASTC, Corresponding Angles of Similar Triangle are Congruent.

OD = OF distance from center to the vertex of a regular octagon are

equal to the radial length of the circumscribing circle and are therefore

equal.

Therefore;

ΔPDO ≅ ΔOMF by Angle-Side-Angle ASA congruency rule

ΔPDO = ΔOMF definition of congruency

  • ΔHOF ≅ ΔDOF by Side-Angle-Side, SAS, congruency rule

ΔHOF = ΔDOF

ΔFHM = ΔHOF - ΔOMF subtraction property

Similarly

ΔDFP = ΔDOF - ΔPDO = ΔHOF - ΔOMF = ΔFHM by substitution property

ΔDFP = ΔFHM

ΔFHM = ΔDFP by symmetric property.

Therefore;


  • <u>ΔFHM ≅ ΔDFP by definition of congruency</u>

Learn more about the properties of a regular octagon here:

brainly.com/question/4503941

3 0
2 years ago
Enter the correct answer in the box. Simplify this expression.
kap26 [50]

Answer:

4^6

Step-by-step explanation:

4^9 \div 4^3

Apply the law of exponents.

=4^{9-3}

=4^6

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Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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