Question

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)

Answer 1

`P_(1)(-14, 12) , P_(2)(5,12)` are 19 units apart

Explanation:

Answer:

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

`P_(1)(x_(1),y_(1)) , P_(2)(x_(2),y_(2))`

`P_(1)(-14, 12) , P_(2)(5,12)\\\\P_(1)(-5, 19) , P_(2)(-12, 19)\\\\P_(1)(-20, 5) , P_(2)(1, 5)\\\\P_(1)(14, 12) , P_(2)(5,12)`

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

`d = \sqrt{(x_(1) - x_(2))^(2) + (y_(1) - y_(2))^(2)}`

For first pair:

`P_(1)(x_(1),y_(1)) , P_(2)(x_(2),y_(2)) = P_(1)(-14, 12) , P_(2)(5,12)\\\\d = \sqrt{(x_(1) - x_(2))^(2) + (y_(1) - y_(2))^(2)}\\\\d = \sqrt{(-14 - 5)^(2) + (12-12)^(2)} = 19`

For second pair:

`P_(1)(x_(1),y_(1)) , P_(2)(x_(2),y_(2)) = P_(1)(-5, 19) , P_(2)(-12,19)\\\\d = \sqrt{(x_(1) - x_(2))^(2) + (y_(1) - y_(2))^(2)}\\\\d = \sqrt{(-5 - 12)^(2) + (19 - 19)^(2)} = 17`

For third pair:

`P_(1)(x_(1),y_(1)) , P_(2)(x_(2),y_(2)) = P_(1)(-20, 15) , P_(2)(1, 5)\\\\d = \sqrt{(x_(1) - x_(2))^(2) + (y_(1) - y_(2))^(2)}\\\\d = \sqrt{(-20 - 1)^(2) + (15 - 5)^(2)} = 23.26`

For 4th pair:

`P_(1)(x_(1),y_(1)) , P_(2)(x_(2),y_(2)) = P_(1)(14, 12) , P_(2)(5,12)\\\\d = \sqrt{(x_(1) - x_(2))^(2) + (y_(1) - y_(2))^(2)}\\\\d = \sqrt{(14 - 5)^(2) + (12 - 12)^(2)} = 9`

Answer 2

Choice a is correct answer.

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).