Determine whether lines bt and mv are parallel, perpendicular, or neither. you must show all of your work to earn full credit. b(1,-4), t(5,12), m(-8,3), v(-4,2)

BT ⊥ MV

The direction vector BT is ...

... T - B = (5, 12) - (1, -4) = (4, 16)

The direction vector MV is ...

... V - M = (-4, 2) - (-8, 3) = (4, -1)

One is not a multiple of the other, so the lines are not parallel.

The dot-product of these direction vectors is

... (4, 16)•(4, -1) = 4·4 + 16·(-1) = 0

When the dot-product is zero, the vectors are perpendicular.

the lines are perpendicular

to determine which case is true we require the slope m of the lines

Parallel lines have equal slopes

Perpendicular slopes are the negative inverse of each other

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = B(1, - 4 ) and (x₂, y₂ ) = T(5, 12 )

= = = 4

repeat with

(x₁, y₁ ) = M(-8, 3 ) and (x₂, y₂ ) = V(-4, 2 )

= = -

4 and - are negative inverses, hence

BT and MV are perpendicular to each other

what is the approximate angle of acb if abc is 25cm and the length of segment bc is 15

step-by-step explanation: