Question

I have 12 unanswered questions can someone please help

Answer 1

(11,-2)

Explanation:

Given:

• 
  `\sf \textsf{ R is the mid point of } \overline{PS}`
• 
  `\sf \textsf{ Q is the mid point of } \overline{RS}`
• P is located at (8,10)
• S is located at (12,-6)

To find:

• The coordinate of Q.

Solution:

We need to find coordinates of R first and we can find the coordinates of Q using the midpoint formula.

The midpoint formula states that the coordinates of the midpoint of a segment with endpoints (x1, y1) and (x2, y2) are:

`\sf Mid-point=\left(( (x_1 + x_2))/(2), ((y_1 + y_2))/(2)\right)`

In this case, the endpoints of the segment are P(8,10) and S(12,-6), so the coordinates of R are:

`\begin{aligned} \textsf{Coordinate of R }&\sf =\left(((8 + 12))/(2), ((10 - 6))/(2)\right) \\\\ &\sf = \left((20)/(2),(4)/(2)\right)\\\\ &\sf = (10,2) \end{aligned}`

Since, the coordinate of R is (10, 2) and Q is the midpoint of R and S.

So, we can need to use midpoint formula again;

In this case, the endpoints of the segment are R(10,2) and S(12,-6), so the coordinates of Q are:

`\begin{aligned} \textsf{Coordinate of Q }&\sf =\left(((10 + 12))/(2), ((2 - 6))/(2)\right) \\\\ &\sf = \left((22)/(2),(-4)/(2)\right)\\\\&\sf = (11,-2)\end{aligned}`

Since, the coordinate of Q is (11, -2).

So, the answer is (11,-2)