Question

(ii) P (a/2,4
is the midpoint of seg AB joining the points A(-6,5) and B(-2, 3).
Find the value of a.​

Answer 1

Answer:

a = -8

Step-by-step explanation:

For any two points forming a straight line, the midpoint of the line is given by the Midpoint formula.

$\dashrightarrow \sf \ M(x, y) = \Bigg\{ \dfrac{x_1 + x_2}{2} , \dfrac{y_1 + y_2}{2} \Bigg\}$

Where M(x, y) is the midpoint of the line formed on joining the points (x₁, y₁) and (x₂, y₂), and x = (x₁ + x₂)/2 and y = (y₁ + y₂)/2.

According to the question;

• Midpoint = P(a/2, 4)

• A = (-6, 5)

• B = (-2, 3)

Now we'll substitute these values in the Midpoint formula.

$\dashrightarrow \sf \ P(x, y) = \Bigg\{ \dfrac{x_1 + x_2}{2} , \dfrac{y_1 + y_2}{2} \Bigg\}$

$\dashrightarrow \sf \ P\Bigg\{\dfrac{a}{2}, \ 4\Bigg\} = \Bigg\{\dfrac{-6 + (-2)}{2} , \dfrac{5 + 3}{2} \Bigg\}$

$\dashrightarrow \sf \ P\Bigg\{\dfrac{a}{2}, \ 4\Bigg\} = \Bigg\{\dfrac{-6 -2}{2} , \dfrac{8}{2} \Bigg\}$

$\dashrightarrow \sf \ P\Bigg\{\dfrac{a}{2}, \ 4\Bigg\} = \Bigg\{-4, \ 4 \Bigg\}$

On equating a/2 with -4 we get; [Because x = (x₁ + x₂)/2]

$\dashrightarrow \sf \ \dfrac{a}{2} = -4$

$\dashrightarrow \sf \ a = -4 \times 2$

$\dashrightarrow \sf \ a = -8$

Therefore the value of 'a' is -8.

Answer 2

Answer:

$:\implies$a = -8.

hope it helps uh :)