Question

Find ​(a) PQ to the nearest tenth and ​(b) the coordinates of the midpoint of PQ. ​P(​-6,​6), ​Q(​4,-1​)

Answer 1

`\Huge \boxed{\mathrm{a) \ 12.21}} \\\\\\\\ \huge \boxed{\mathrm{b) \ -1, \ (5)/(2)}}`

`\rule[225]{225}{2}`

Explanation:

(a)

We can use Pythagorean theorem to solve for the length of PQ.

`PQ=√(10^2 +7^2 )`

`PQ=√(149) \approx 12.2066`

The length of PQ is approximately 12.21.

(b)

We can find the midpoint with the midpoint formula:

`\displaystyle (x_1 + x_2 )/(2), \ (y_1+y_2)/(2)`

`\displaystyle (-6+4 )/(2), \ (6+-1)/(2)`

`\displaystyle (-2 )/(2), \ (5)/(2)`

`\displaystyle -1, \ (5)/(2)`

`\rule[225]{225}{2}`

Answer 2

a) PQ = 12.2

b) M (-1, 2.5)

Explanation:

a) PQ

use pythagorean PQ =
`√((6+4)^2 +(6+1)^2)`

PQ =
`√(149)` = 12.2

b) Midpoint

Mx = (-6 + 4)/2 = -1

My = (6 + -1)/2 = 2.5