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rusak2 [61]
3 years ago
8

The endpoints of CD are C(−4, 7) and D(0,−3).

Mathematics
2 answers:
Yakvenalex [24]3 years ago
8 0

Answer:

coordinates of CD is (-2, 2)

Step-by-step explanation:

Formula:

Let (x₁,y₁) and (x₂,y₂) be the end points of two coordinates  and (x,y) be the mid points. The value of (x,y) is given by,

x = (x₁ + x₂)/2 and y = (y₁ + y₂)/2

<u>To find the mid point of CD</u>

C(-4, 7) and D(0, -3)

x₁  = -4 and  x₂ = 0

y₁ = 7 and  y₂ = -3

x=(x₁ + x₂)/2 = (-4 + 0)/2 = (-4)/2 =-2

(y₁ + y₂)/2 = (7 + -3)/2= 4/2 = 2

Therefore coordinates of CD is (-2, 2)

tino4ka555 [31]3 years ago
4 0

Midpoint =(\frac{x_{2}+x_{1}}{2},\frac{y_{2}+y_{1}}{2})

Answer:

Midpoints of line CD are (-2,2).

Step-by-step explanation:

The midpoints is given by

Midpoint =(\frac{x_{2}+x_{1}}{2},\frac{y_{2}+y_{1}}{2})

As given

The endpoints of CD are C(−4, 7) and D(0,−3).

Putting values in the above

Midpoint =(\frac{0-4}{2},\frac{-3+7}{2})

Midpoint =(\frac{-4}{2},\frac{4}{2})

Midpoints = (-2,2)

Therefore midpoints of line CD are (-2,2).

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Answer:

The correct option is;

C. 3. ∠BDE ≅∠BAC, Corresponding Angles Postulate 4. ∠B ≅ ∠B Reflexive Property of Equality

Step-by-step explanation:

The two column proof can be written as follows;

Statement,                         Reason

1. \overline{DE} \parallel \overline{AC},                           Given

2. \overline {AB} is a transversal ,         Conclusion from statement 1.

We note that ∠BDE  and ∠BAC are on the same side of the transversal relative to the parallel lines, and are therefore, corresponding angles.

Therefore, we have;

3. ∠BDE ≅∠BAC,                 Corresponding Angles Postulate

Also

4. ∠B ≅ ∠B,                           Reflexive Property of Equality

In the two triangles, ΔABC and ΔDBE, we have ∠BDE ≅∠BAC and ∠B ≅ ∠B,

From ∠BDE + ∠B + ∠BED = 180°

∠BAC + ∠B +  ∠BCA = 180°

Therefore, ∠BED = ∠BCA Substitution property of equality

Which gives;

5, ΔABC ~ ΔDBE,          Angle Angle Similarity Postulate

6. BD/BA = BE/BC,      Converse of the Side-Side-Side Similarity Theorem

5 0
3 years ago
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