Question

Pq has length of 17 units with p(-4,7).If x and y coordinates are both grater than x and y coordinates of p what are the possible integer value coordinated of q

Answer 1

Given P coordinate as (-4,7). Let Q coordinate be $(x_2,y_2)$.

Distance between P and Q is 17 units.

Firstly, we will find the distance between P and Q using distance formula.

For the given points say $(x_1,y_1) and (x_2,y_2)$ the distance is given by the formula $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Since, PQ = 17 units

$(-4,7)(x_2,y_2) = 17$

$\sqrt{(x_2+4)^2+(y_2-7)^2}= 17$

${(x_2+4)^2+(y_2-7)^2}=289$

So, we have to find the perfect squares so that the sum is 289.

Only 64 and 225 are the possibilities such that 64+225 = 289.

So, the possible coordinates are:

(8,15) (8,-15) (-8,-15) (-8,15) (15,8) (15,-8) (-15,-8) and (-15,8)

Since, it is given that 'x' and 'y' coordinates are both greater than x and y coordinates of P.

So, (8,15) and (5,18) are the possibilities to be coordinates of Q.