The coordinates of the vertices of △def are d(−4, 1), e(3, −1), and f(−1, −4). which statement correctly describes whether △def is a right triangle? △def is not a right triangle because no two sides are perpendicular. △def is a right triangle because de¯¯¯¯¯ is perpendicular to df¯¯¯¯¯. △def is a right triangle because df¯¯¯¯¯ is perpendicular to ef¯¯¯¯¯. △def is a right triangle because de¯¯¯¯¯ is perpendicular to ef¯¯¯¯¯ .

â–łDEF is not a right triangle because no two sides are perpendicular. There are two ways to determine if DEF is a right triangle. You can use the pythagorean theorem to see of a^2 + b^2 = c^2, or you can calculate the slope of each pair of lines to see if their product is -1. I'll demonstrate both methods, but given the available options, I suspect that the product of the slopes is the one you need. Slope method. Slope of DE = (1-(-1))/(-4-3) = 2/-7 = -2/7 Slope of EF = (-1-(-4))/(3-(-1)) = 3/4 Slope of DF = (1-(-4))/(-4-(-1)) = 5/-3 = -5/3 Since we're looking for -1 as a product and we have 2 negative slopes and 1 positive slope, we only need to check DE against EF and EF against DF. So -2/7 * 3/4 = -6/28 = -3/14. This isn't -1, so not perpendicular. 3/4 * -5/3 = -15/12 = -5/4. Still not -1, so not perpendicular. Since no sides of perpendicular to any other sides, DEF is not a right triangle. Now for the pythagorean theorem method. First, let's take a look at the length of the 3 sides of DEF. Actually, we just need to look at the square of the lengths of each side. So square of length DE = (-4 - 3)^2 + (1 - (-1))^2 = -7^2 + 2^2 = 49 + 4 = 53. square of length EF = (3-(-1))^2 + (-1-(-4))^2 = 4^2 + 3^2 = 16+9 = 25 square of length DF = (-4-(-1))^2 + (1-(-4))^2 = -3^2 + 5^2 = 9 + 25 = 34 The longest side is DE, so lets add up the squares of the other 2 sides to see if they equal the square of DE. 25 + 34 = 59. And 59 is not equal to 53. So we know that triangle DEF is NOT a right triangle. Now let's look at the options and see what's correct. â–łDEF is not a right triangle because no two sides are perpendicular. * This is a true statement. So it's the correct answer. The remaining 3 other options all claim that one side is perpendicular to another and as such are incorrect.

You need to include the original coordinates of the triangle to answer this. and how much does it translate (move left right up down)