Question

A translation moves A(2,3) onto An (4,8) what are the coordinates of B’ the image of B(4,6) under the same translation

Answer 1

Answer:

(1.931, 5.172)

Step-by-step explanation:

Given that the image of A(2,3) is A'(4,8).

Now, the equation of straight line passing through A and A' is

$\frac{(y-3)}{(8-3)} =\frac{(x-2)}{(4-2)}$

⇒(y-3) =2/5(x-2)

⇒y =2x/5 +(3-4/5)

⇒ y= 2x/5 +11/5 ......(1)

And the mid point of A and A' is ($\frac{2+4}{2},\frac{3+8}{2}$)≡(3,5.5)

Now, Equation of perpendicular straight line to (1), is given by

y= -5x/2 +c ....... (2) {Since, the product of slopes of two mutually perpendicular straight line is always -1}

Now, equation (2) passes through (3, 5.5) point.

Hence, 5.5 =-5×3/2 +c, ⇒ c=13.

So, the mirror straight line is y=-5x/2 +13 ......(3)

Now, parallel straight line to (1), is given by

y=2x/5 +c' and the point (4,6) satisfies it.

So, 6=2×4/5 +c', ⇒ c' =22/5.

So, the equation becomes y=2x/5 +22/5 ........ (4)

Now, solving equations (3) and (4) we get

-5x/2 +13=2x/5 +22/5

⇒ 29x/10 =43/5

⇒ x=86/29=2.965 and from (4), we get y=2/5(86/29) +22/5 =172/145+22/5 =5.586

Hence, the point becomes (2.965, 5.586)

If (h,k) be the required image, then (2.965, 5.586) point must be the mid point of (h,k) and (4,6).

Therefore, (h+4)/2 =2.965 ⇒ h= 1.931 and (k+6)/2 =5.586, ⇒k=5.172.

So, the image point is (1.931, 5.172). (Answer)