Question

P and Q have coordinates (-2,3) and (5,4) respectively. Reflect P inthe X-axis to P' and Q in tha Y-axis to Q' .Find the distance between P'Q'.​

Answer 1

Step-by-step explanation:

Hey, there!!

Let's simply work with it,

The given coordinates are, P(-2,3) and Q(5,4).

Now, finding the P' and Q'.

Reflection on x- axis .

P(x,y)---------> P' (x,-y)

P (-2,3)----------> P'(-2,-3)

Now, let's find Q'

Reflection on y-axis.

Q(x,y)----------> Q'(-x,y)

Q(5,4)---------> Q'(-5,4)

Now, The points are P'(-2,-3) and Q'(-5,4)

By distance formulae,

$P'Q' = \sqrt{( {x2 - x1)}^{2} + ( {y2 - y1)}^{2} }$

Putting their values,

$P'Q' = \sqrt{( { - 5 + 2)}^{2}( {4 + 3)}^{2} }$

$P'Q' = \sqrt{( { - 3)}^{2} + ( {7)}^{2} }$

Simplifying them we get,

$pq = \sqrt{58}$

Therefore, the distance between P'and Q' is root under 58 units.

Hope it helps...