8. J, H, and G are mid points. If AB = 10, JH = 8, and BH = 6, what is the perimeter of ABC?

These questions require using a graph for equations.
9. What is the distance between points A (-2, -6) and B ( 1, -2)

10. For Triangle ABC, AB=9, AC= 8, and BC= 7. List the angles from least to greatest.
asked Feb 2, 2013 in GEOMETRY

+1 vote

9). A(-2, -6) and B(1, -2)

Distance Formula: Given the two points (x1, y1) and (x2, y2), the distance between these points is given by the formula:

d = √[(1- (-2))2 + (-2 - (-6))2]

d = √[(1 + 2)2 + (-2 + 6)2]

d = √[(3)2 + (4)2]

d = √[(9) + (16)]

d = √[25]

d = 5.

There fore the distance is 5.

• (8).

Consider, that, J, H,and G are the mid points of AB, BC, and AC.

From, the given data AB = 10, JH = 8, and BH = 6.

BC = BH + HC

= BH + BH                       (Since, H is the mid point of BC)

= 2BH

= 2 * 6

= 12

⇒ BC = 12.

From, mid point theorem, if JH = 8 if and only if AC = 2JH =2 * 8 = 16.

⇒ AC = 16.

Perimeter of triangle ABC = AB + BC + AC

= 10 + 12 + 16

= 38 units.

Therefore, perimeter of triangle ABC is 38 units.

• (10).

The smallest angle is opposite to the smallest side.

Sides of triangle ABC :

AB = 9, AC = 8, and BC = 7.

The smallest side of the triangle ABC is BC.

The smallest angle is opposite to the smallest side.

Angle A is opposite to the smallest side BC.

So, the smallest(least) angle is angle A.

Next AC > BC.

SO, angle B > angle A.

Next AB > AC.

SO, angle C > angle B.

Therefore, the least angle is  angle A, and the greatest angle is angle C.

The angles from least to greatest : A < B < C.