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

Answer:

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).

Answer 2

Answer:

$P_{1}(-14, 12) , P_{2}(5,12)$ are 19 units apart

Step-by-step 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:

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