Which points are 19 units apart? (–14, 12) and (5, 12) (–5, 19) and (–12, 19) (–20, 5) and (1, 5) (14, 12) and (5, 12)

are 19 units apart

Step-by-step explanation:

We are given four pair of points and we have to find which points are 19 units apart:

Using distance formula to find how far the points are from each other

For first pair:

For second pair:

For third pair:

For 4th pair:

Choice a is correct answer.

Step-by-step explanation:

We have given four set of points.

(a)  (-14,12) and (5,12)

(b)  (-5,19) and (-12,19)

(c)  (-20,5) and (1,5)

(d)  (14,12)  and (5,12)

We have to find the distance between each set of points.

The formula for distance is:

d = √(x₂-x₁)²+(y₂-y₁)²

The set of points which have 19 units distance is our answer.

For (a):

d =√(5-(-14)²+(12-12)²

d = √(5+14)²+(0)²

d = 19 units

for (b) :

d = √(-12-(-5))²+(19-19)²

d = √(-12+5)²+(0)²

d = √(-7)²

d = 7 units

for (c):

d = √(1-(-20)²+(5-5)²

d = √(1+20)²+(0)²

d = 21 units

for (d):

d =√(5-14)²+(12-12)²

d = √(-9)²+(0)²

d = 9 units

Hence , correct choice is (a).

34.5 cm

step-by-step explanation:

generally for a circular segment of angle, θ° and radius r

arc length

= (θ/360) x circumference

= (θ/360) x 2πr

in our case, θ = 60°, π=3.142 and r = 33 cm

substitute into above formula

arc length

= (60/360) x 2(3.142)( 33) = 34.5 cm