Question

100 points! Mhanifa please help! Look at the picture attached. I will mark brainliest. Random answers will be reported guys.

Answer 1

Answer:

Given points are,

A = (-4,6)

B = (6,6)

C = (6,2)

To find out the circumcenter we have to solve any two bisector equations and find out the intersection points.

So, mid point of AB = [(- 4 + 6)/2, (6 + 6)/2] = (1, 6)

Slope of AB = [(6 − 6)/(6 + 4)] = 0

The slope of the bisector is the negative reciprocal of the given slope.

So, the slope of the perpendicular bisector = 0

Equation of AB with slope 0 and the coordinates (1, 6) is,

(y + 4) = 1(x – 6)

x – y = - 2……………(1)

Similarly, for AC

Mid point of AC = [(- 4 + 6)/2, (6 + 2)/2] = (1, 4)

Slope of AC = [(2 − 6)/(6 + 4)] = - 4/10

The slope of the bisector is the negative reciprocal of the given slope.

So, the slope of the perpendicular bisector = 10/4

Equation of AC with slope 10/4 and the coordinates (1, 4) is,

(y + 4) = -1(x – 4)

y – 3 = -x + 4

x + y = 7………………(2)

By solving equation (1) and (2),

(1) + (2) ⇒ 2x = 10;

Or, x = 5

Substitute the value of x in to (1)

3 – y = -1

y = 3 + 1 = 4

Thus, the circumcenter is (5, 4).

Answer 2

Steps by explanation:

for second one

centroid ={(1+3+5)/3,(2+4+0)/3}=(9/3,6/3)

=(3,2)