Sagot :
MIDPOINT
-In order to find the midpoint of a segment whose endpoints are given, use the midpoint formula:
- [tex]\boxed{\tt\:M=\bigg(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\bigg)}[/tex]
1. A(6, 8) and B (12, 10)
- [tex]\tt\:M=\bigg(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\bigg)[/tex]
- [tex]\tt\:M=\bigg(\frac{6+12}{2}, \frac{8+10}{2}\bigg)[/tex]
- [tex]\tt\:M=\bigg(\frac{18}{2}, \frac{18}{2}\bigg)[/tex]
- [tex]\tt\red{M=(9,9)}[/tex]
2. C(5, 11) and D (9, 5)
- [tex]\tt\:M=\bigg(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\bigg)[/tex]
- [tex]\tt\:M=\bigg(\frac{5+9}{2}, \frac{11+5}{2}\bigg)[/tex]
- [tex]\tt\:M=\bigg(\frac{14}{2}, \frac{16}{2}\bigg)[/tex]
- [tex]\tt\red{M=(7,8)}[/tex]
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3. K(-3, 2) and L (11, 6)
- [tex]\tt\:M=\bigg(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\bigg)[/tex]
- [tex]\tt\:M=\bigg(\frac{-3+11}{2}, \frac{2+6}{2}\bigg)[/tex]
- [tex]\tt\:M=\bigg(\frac{8}{2}, \frac{8}{2}\bigg)[/tex]
- [tex]\tt\red{M=(4,4)}[/tex]
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4. R(-2, 8) and S (10, -6)
- [tex]\tt\:M=\bigg(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\bigg)[/tex]
- [tex]\tt\:M=\bigg(\frac{-2+10}{2}, \frac{8+(-6)}{2}\bigg)[/tex]
- [tex]\tt\:M=\bigg(\frac{8}{2}, \frac{2}{2}\bigg)[/tex]
- [tex]\tt\:M=\bigg(\frac{8}{2}, \frac{2}{2}\bigg) \: [/tex]
- [tex]\tt\red{M=(4,1)}[/tex]
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5. P (-5,-1) and Q (8, 6)
- [tex]\tt\:M=\bigg(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\bigg)[/tex]
- [tex]\tt\:M=\bigg(\frac{-5+8}{2}, \frac{-1+6}{2}\bigg)[/tex]
- [tex]\tt\red{M=\bigg(\frac{3}{2}, \frac{5}{2}\bigg)}[/tex]
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6. M (-9, 15) and N (-7, 3)
- [tex]\tt\:M=\bigg(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\bigg)[/tex]
- [tex]\tt\:M=\bigg(\frac{-9+(-7)}{2}, \frac{15+3}{2}\bigg)[/tex]
- [tex]\tt\:M=\bigg(\frac{-16}{2}, \frac{18}{2}\bigg)[/tex]
- [tex]\tt\red{M=(-8,9)}[/tex]
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7. Q (0, 8) and R (-10, 0)
- [tex]\tt\:M=\bigg(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\bigg)[/tex]
- [tex]\tt\:M=\bigg(\frac{0+(-10)}{2}, \frac{8+0}{2}\bigg)[/tex]
- [tex]\tt\:M=\bigg(\frac{-10}{2}, \frac{8}{2}\bigg)[/tex]
- [tex]\tt\red{M=(-5,4)}[/tex]
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8. D (12, 5) and E (3, 10)
- [tex]\tt\:M=\bigg(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\bigg)[/tex]
- [tex]\tt\:M=\bigg(\frac{12+3}{2}, \frac{5+10}{2}\bigg)[/tex]
- [tex]\tt\red{M=\bigg(\frac{15}{2}, \frac{15}{2}\bigg)}[/tex]
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9. X (-7, 11) and Y (-9, 3)
- [tex]\tt\:M=\bigg(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\bigg)[/tex]
- [tex]\tt\:M=\bigg(\frac{-7+(-9)}{2}, \frac{11+3}{2}\bigg)[/tex]
- [tex]\tt\:M=\bigg(\frac{-16}{2}, \frac{14}{2}\bigg)[/tex]
[tex]\tt\red{M=(-8,7)}[/tex]
10. P (-3, 10) and T (-7, 2)
- [tex]\tt\:M=\bigg(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\bigg)[/tex]
- [tex]\tt\:M=\bigg(\frac{-3+(-7)}{2}, \frac{10+2}{2}\bigg)[/tex]
- [tex]\tt\:M=\bigg(\frac{-10}{2}, \frac{12}{2}\bigg)[/tex]
- [tex]\tt\red{M=(-5,6)}[/tex]
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