Respuesta :

Answer:

Step-by-step explanation:

Solution

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Given a triangle ABC with vertices A(2,3),B(4,−1),C(1,2)

Let AD be the perpendicular from the vertex A.

Now, slope of BC i.e.m

1

​

=

x

2

​

−x

1

​

y

2

​

−y

1

​

​

=

1−4

2−(−1)

​

=

−3

3

​

=−1

Let m

2

​

 be the slope of AD.

Since, AD is perpendicular to BC.

m

1

​

m

2

​

=−1

−1m

2

​

=−1

⇒m

2

​

=1

So, slope of AD is 1.

Equation of line having one coordinate and slope is given by  

y−y

1

​

=m(x−x

1

​

)

So, equation of AD is

y−3=1(x−2)

⇒y=x+1

⇒−x+y−1=0

We know that the perpendicular distance of a line Ax+By+C=0 from point (x

1

​

,y

1

​

) is given by

d=

A

2

+B

2

​

∣Ax

1

​

+By

1

​

+C∣

​

Now , length of AD from vertex A(2,3) is

∣

(−1)

2

+1

2

​

−3+2−1

​

∣

=∣

2

​

−2

​

∣

=

2

​

Hence, length of altitude AD is  

2

semsee45

Answer:

A' = (-2, -4)

B' = (-7, -6)

C' = (0, 0)

Step-by-step explanation:

Vertices of triangle ABC:

  • A = (2, -3)
  • B = (-3, -5)
  • C = (4, 1)

Given mapping rule:

(x, y) → (x - 4, y - 1)

This notation tells you that the x-coordinate is translated 4 units to the left, and the y-coordinate is translated 1 unit down.

Substitute the coordinates of each point into the mapping rule to find the vertices of triangle A'B'C':

⇒ A' = (2 - 4, -3 - 1) = (-2, -4)

⇒ B' = (-3 - 4, -5 - 1) = (-7, -6)

⇒ C' = (4 - 4, 1 - 1) = (0, 0)

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