Question

If the midpoint of A (a, b) and B(-9, 6) is M(-3, 5):
Find the value of a.

Answer 1

(-6,5.5)

Explanation:

(-9,6)-(-3,5)

-9+-3/2 6+5/2

x=-6 y=5.5

Answer 2

`\huge{ \fbox{ \text{3}}}`

Explanation:

`\sf{A ( \: a \:, b \: )\: \longrightarrow{ \: (x1 \:, y1)}}`

`\sf{ \: B( - 9 \: 6) \: \longrightarrow{ (x2 \:, y2)}}`

`\boxed{ \sf{midpoint = ( (x1 + x2)/(2) \: , (y1 + y2)/(2) )}}`

`\mapsto{ \sf{( - 3 \:, 5 \: ) \: = \: ( (a + ( - 9))/(2) \:, (b + 6)/(2)}})`

`\mapsto{ \sf{( - 3 \:, 5) \: = \: ( \: (a - 9)/(2) \:, (b + 6)/(2) )}}`

`\sf{ \mapsto{ - 3 = (a - 9)/(2) }}`

Solve for a

`\mapsto{ \sf{ - 6 = a - 9}}`

`\mapsto{ \sf{a - 9 = - 6}}`

`\mapsto{ \sf{a = - 6 + 9}}`

`\mapsto{ \sf{a = 3}}`

The value of a is 3

Hope I helped!

Best regards! :D

~
`\text{TheAnimeGirl}`