On a coordinate plane, triangle A B C is shown. Point A is at (negative 1, 1), point B is at (3, 2), and points C is at (negative 1, negative 1) If line segment BC is considered the base of triangle ABC, what is the corresponding height of the triangle? 0.625 units 0.8 units 1.25 units 1.6 units

1.6 units

Step-by-step explanation:

A(-1, 1)

B(3,2)

C(-1, -1)

BC slope: (2 - (-1))/(3 - (-1)) = 3/4

Equation of a line that pass through A(-1, 1) with slope -4/3 (so that it is perpendicular to segment BC)

y - y1 = m(x - x1)

y - 1 = -4/3(x + 1)

Equation of the line that passes through segment BC:

y - y1 = m(x - x1)

y - 2 = 3/4(x - 3)

These two lines intersect is found solving the next system of equations:

y - 1 = -4/3(x + 1) (eq. 1)

y - 2 = 3/4(x - 3) (eq. 2)

Subtractin eq. 2 to eq. 1, we get :

-1 + 2 = -4/3(x + 1) - 3/4(x - 3)

1 = -4/3x - 4/3 - 3/4x + 9/4

1 + 4/3 - 9/4 = -25/12x

1/12*(-12/25) = x

-0.04 = x

Replacing into eq. 1:

y - 1 = -4/3(-0.04 + 1)

y = -1.28 + 1

y = -0.28

The height of the triangle is the distance between A(-1, 1) and (-0.04, -0.28)

d = √[(-1 - (-0.04))² + (1 - (-0.28))²] = 1.6 units

a 4/6 = 9/12   not proportional

step-by-step explanation:

to find which are not proportional, we can use cross products

if it is true, they are proportional.   if it is not true, they are not proportional.

a 4/6 = 9/12

4* 12 = 6*9

48 = 54

not this is not proportional  

b 2/3 = 12/18  

2* 18 = 3 * 12

36 = 36

this is proportional

c 5/4 = 10/8  

5*8 = 4*10

40 = 40

this is proportional

d 7/5 = 35/25

7*25 = 5 * 35

175 = 175

is proportional

0.50 , 0.75

step-by-step explanation: