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

(2x + 16) + (x) = 180

step-by-step explanation:

given,

abcd is a quadrilateral inscribed in a circle

angle a is labeled x plus 16, (x + 16)

angle b is labeled x degrees, (x)

angle c is labeled 6x minus 4, (6x – 4)

angle d is labeled 2x plus 16, (2x + 16)

what equation can be used to solve for angle b?

we know that the sum of the opposite angles of a simple quadrilateral inscribed in a circle is 180 degrees.

angle b is opposite angle d

therefore, angle b + angle d = 180

(x) + (2x + 16) = 180 

same as (2x + 16) + (x) = 180