To find the mean of the abscissa of point [tex]\(P\)[/tex] and the ordinate of point [tex]\(Q\)[/tex], follow these steps:
1. Identify the abscissa (x-coordinate) of point [tex]\(P\)[/tex] and the ordinate (y-coordinate) of point [tex]\(Q\)[/tex]:
The coordinates of point [tex]\(P\)[/tex] are [tex]\((7, 5)\)[/tex], where:
[tex]\[
P_x = 7 \quad (\text{abscissa of } P)
\][/tex]
The coordinates of point [tex]\(Q\)[/tex] are [tex]\((-2, 7)\)[/tex], where:
[tex]\[
Q_y = 7 \quad (\text{ordinate of } Q)
\][/tex]
2. Calculate the mean of these two values:
The formula for the mean of two numbers, [tex]\( a \)[/tex] and [tex]\( b \)[/tex], is given by:
[tex]\[
\text{Mean} = \frac{a + b}{2}
\][/tex]
Substitute [tex]\( P_x \)[/tex] and [tex]\( Q_y \)[/tex] into the formula:
[tex]\[
\text{Mean} = \frac{P_x + Q_y}{2} = \frac{7 + 7}{2}
\][/tex]
3. Perform the arithmetic operations:
Adding 7 and 7:
[tex]\[
7 + 7 = 14
\][/tex]
Dividing the sum by 2:
[tex]\[
\frac{14}{2} = 7
\][/tex]
Therefore, the mean of the abscissa of point [tex]\(P\)[/tex] and the ordinate of point [tex]\(Q\)[/tex] is:
[tex]\[
7.0
\][/tex]
Thus, the final answer is [tex]\( \boxed{7.0} \)[/tex].
