What is true about △ABC? Select three optionsA) AB ⊥ ACB) The triangle is a right triangle. C) The triangle is an isosceles triangle. D) The triangle is an equilateral triangle.E) BC ∥ AC

Accepted Solution

Answer:A) AB ⊥ ACB) The triangle is a right triangle.C) The triangle is an isosceles triangleStep-by-step explanation:we know thatthe formula to calculate the distance between two points is equal to [tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex] step 1Find the distance ABwe have[tex]A(-1,3), B(-5,-1)[/tex]substitute in the formula[tex]d=\sqrt{(-1-3)^{2}+(-5+1)^{2}}[/tex] [tex]d=\sqrt{(-4)^{2}+(-4)^{2}}[/tex] [tex]d_A_B=\sqrt{32}\ units[/tex] step 2Find the distance BCwe have[tex]B(-5,-1),C(3,-1)[/tex]substitute in the formula[tex]d=\sqrt{(-1+1)^{2}+(3+5)^{2}}[/tex] [tex]d=\sqrt{(0)^{2}+(8)^{2}}[/tex] [tex]d_B_C=8\ units[/tex] step 3Find the distance ACwe have[tex]A(-1,3),C(3,-1)[/tex]substitute in the formula[tex]d=\sqrt{(-1-3)^{2}+(3+1)^{2}}[/tex] [tex]d=\sqrt{(-4)^{2}+(4)^{2}}[/tex] [tex]d_A_C=\sqrt{32}\ units[/tex] step 4Compare the length sides of triangle[tex]d_A_B=\sqrt{32}\ units[/tex] [tex]d_B_C=8\ units[/tex] [tex]d_A_C=\sqrt{32}\ units[/tex] thereforeThe triangle ABC is an isosceles triangle, because has two equal sidesThe triangle ABC is a right triangle because satisfy the Pythagoras theorem[tex]BC^2=AB^2+AC^2[/tex][tex]8^2=(\sqrt{32})^2+(\sqrt{32})^2[/tex][tex]64=32+32[/tex][tex]64=64[/tex] ----> is true (Is a right triangle)AB ⊥ AC because in a right triangle the legs are perpendicular