2. The coordinates of the vertices of ΔARC are A(3,3), R(1,-1), and C(-2,1). Angela is trying to determine whether this shape is a right triangle or not. She has made a mistake in the work below the graph. Explain the mistake and show the correct solution. Angela’s solution:

slope of AR = (3-(-1))/(3-1)=3/2

slope of RC = (1-(-1))/(-2-1)=2/(-3)=-2/3

slope of AC = (3-1)/(3-(-2))=2/5

Since AR and RC are opposite reciprocal slopes, those two sides are perpendicular, and the triangle is a right triangle.

Her mistake was in the slope for segment AR, (3 - (-1)/(3 -1) = 4/2 ≠ 3/2

Step-by-step explanation:

The steps for obtaining the slope is given as follows;

Where;

(x₁, y₁) and (x₂, y₂) are the coordinates of the endpoints of the line

The coordinates of the vertices are;

A(3, 3), R(1, -1), and C(-2, 1)

Slope of AR = (3 - (-1))/(3 - 1) = (3 + 1)/(3 - 1) = 4/2 = 2

The slope of RC = (-1 - 1)/(1 - (-2)) = -2/(1 + 2) = -2/3

The slope of AC = (3 - 1)/(3 - (-2)) = 2/(3 + 2) = 2/5

Therefore, her mistake was the value of the double negation in the numerator when finding the slope of AR is 4 rather than 3

answer: e 9, 5.75

step-by-step explanation:

step 1

find the variation ab in the x coordinate

delta x=(x2-x1)=10-> 8 units

find the variation ab  in the y coordinate 

delta y=(y2-y1)=6-> 2 units

step 2

find the coordinates point c

  x coordinate 

cx=ax+delta x*2/> cx=2+8*(2/> cx=3

  y coordinate 

cy=ay+delta y*2/> cy=4+2*(2/> cy=4.25

the coordinates of point c are (3,4.25)

step 3

find the coordinates point d

  x  coordinate 

dx=ax+delta x*4/> dx=2+8*(4/> dx=4

  y  coordinate 

dy=ay+delta y*4/> dy=4+2*(4/> dy=4.5

the coordinates of point d are (4, 4.5)

step 4

find the coordinates point e

  x  coordinate 

ex=ax+delta x*4/> ex=2+8*(6/> ex=5

  y  coordinate 

ey=ay+delta y*4/> ey=4+2*(6/> ey=4.75

the coordinates of point e are (5, 4.75)

step 5

find the coordinates point f

  x  coordinate 

fx=ax+delta x*4/> fx=2+8*(8/> fx=6

  y  coordinate 

fy=ay+delta y*4/> fy=4+2*(8/> fy=5

the coordinates of point f are (6,5)

step 6

find the coordinates point g

  x  coordinate 

gx=ax+delta x*4/> gx=2+8*(10/> gx=7

  y  coordinate 

gy=ay+delta y*4/> gy=4+2*(10/> gy=5.25

the coordinates of point g are (7,5.25)

step 7

find the coordinates point h

  x  coordinate 

hx=ax+delta x*4/> hx=2+8*(12/> hx=8

  y  coordinate 

hy=ay+delta y*4/> hy=4+2*(12/> hy=5.5

the coordinates of point h are (8,5.5)

step 8

find the coordinates point i

  x  coordinate 

ix=ax+delta x*4/> ix=2+8*(14/> ix=9

  y  coordinate 

iy=ay+delta y*4/> iy=4+2*(14/> iy=5.75

the coordinates of point i are (9,5.75)

- r3ktforgood ☕