State whether the following coordinates on a cartesian plane form an acute, obtuse or right triangle: a) (-1, 1), (7,-2) and (1,-5) b) (0,6), (1, 2) and (5,3)

a) Acute triangle

b) Right triangle

Step-by-step explanation:

∵ A triangle having sides a, b and c is called,

Acute : If a² + b² > c² or a² + c² > b² or b² + c² > a²,

Obtuse : if a² + b² < c² or a² + c² < b² or b² + c² < a²

Right : a² + b² = c² or a² + c² = b² or b² + c² = a²,

a) Let A≡(-1, 1), B≡(7,-2) and C≡(1,-5),

By the distance formula,

Similarly,

∵ The sum of any two sides is greater than third side,

So, ABC is a triangle,

Now,

⇒ ABC is an acute triangle.

b) Let P≡(0,6), Q≡(1,2) and R≡(5,3),

By the distance formula,

PQ = √17 unit,

QR = √17 unit,

RP = √34 unit,

∵ The sum of any two sides of PQR is greater than third side,

⇒ PQR is a triangle ,

Also,

Hence, PQR is a right triangle.

given : the shape of his satellite can be modeled by   where x and y are modeled in inches.

now,the given equation   is a equation of parabola.

here, coefficient of x is positive, hence the parabola opens rightwards.

on comparing this equation with standard equation , we get

in standard equation, coordinates of focus=(0,m)

thus for given equation coordinates of focus=(0,1.5)

step-by-step explanation:

yes.. it's proven to be 36.