Question

How do i solve this??

Answer 1

Answer:

J (3; 9)

Step-by-step explanation:

Imagine each distance like a triangle and use Pythagorean theorem.

To illustrate I drew triangle ΔLON in the picture

Finding the distance between LN.

LO = $y_{L} - y_{O}$ = 5 - 1 = 4

NO = $x_{N} - x_{O}$ = 5 - 4 = 1

According to Pythagorean theorem

$LN^{2} = LO^{2} + NO^{2}$

$LN^{2}$ = $4^{2} + 1^{2}$ = 17

LN  = $\sqrt{17}$ (LN > 0)

Since ΔMLN ≅ ΔKLJ, JL = LN (they are clearly equal triangles)

Mark J coordinates as (x; y)

Draw another triangle JOL, ∠JOL = 90°)

OJ is parallel with x axis and OL is parallel with y axis.  O coordinates then are (4; y)

OL  = y - 5

OJ = 4 - x

Note that ΔLON = ΔJOL, so OL is the same as LO and therefore

OL = LO = y - 5 = 4;

y = 9

OJ = NO = 4 - x = 1

x = 3

So the coordinates of J are (3; 9)

Similarly find the coordinates of K