Question

The midpoint of PQ is (–6, –3). One endpoint of PQ is P(–1, –4). What are the coordinates of Q?. A.. Q(–11, –2). B.. Q(–3.5, –3.5). C.. Q(2, 11). D.. Q(11, 2).

Answer 1

Option A is correct.

Explanation:

Coordinates of the mid point of PQ = ( -6 , -3 )

Coordinate of the point P = ( -1, -4 )

We have to find coordinate of point Q(x , y)

We use the Section formula of mid point.

`Coordinate\:of\:Mid-Point=((x_1+x_2)/(2),(y_1+y_2)/(2))`

Thus, we have

`((x_1+x_2)/(2),(y_1+y_2)/(2))=(-6,-3)`

`\implies(x_1+x_2)/(2)=-6` and
`(y_1+y_2)/(2)=-3`

`\implies(-1+x)/(2)=-6` and
`(-4+y)/(2)=-3`

`\implies-1+x=-12` and
`-4+y=-6`

`\implies x=-12+1` and
`y=-6+4`

`\implies x=-11` and
`y=-2`

So, Coordinate of point Q is ( -11 , -2 )

Therefore, Option A is correct.

Answer 2

The midpoint of PQ : ( - 6 , - 3 ).
P ( - 1, - 4 ); Q ( x , y )
- 6 = ( - 1 + x ) / 2
- 1 + x = - 12
x = - 12 + 1 = - 11
- 3 = ( - 4 + y ) / 2
- 4 + y = - 6
y = - 6 + 4 = - 2
Answer: A ) Q ( - 11, - 2 )