Coordinates of the vertices! I really need help!

  GH = 5; ∠H = 90°

Step-by-step explanation:

As with many multiple-choice questions, you only need to use a bit of sense to choose the correct answer. It can help to plot the points on a graph. This immediately shows you the location of the right angle, and the lengths of the sides.

∠H = 90° narrows the choices to the first two. GH = 5 eliminates the second choice. That is sufficient for finding the correct answer.

The appropriate answer choice is the first one.

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Unnecessary further working

You know the tangent of angle G is the ratio of the opposite side (6) to the adjacent side (5). That is, ...

  ∠G = arctan(6/5) ≈ 50°

  ∠I = 90° -∠G = 40°

The length of GI is found using the Pythagorean theorem:

  GI² = GH² +HI² = 5² +6² = 61

  GI = √61 ≈ 7.81

step-by-step explanation:

∆abc has the points a(1, 7), b(-2, 2), and c(4, 2) as its vertices. formed with the point d(1, 2) as its third vertex, then ∆abd is triangle.

just sum

10 + 10 = 20