In the rectangular coordinate system, given three points a (1,2,3), B (2,0,4) C (2, - 1,3), find the area of △ ABC

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• 1. In Cartesian coordinates, if a (2,0), B (- 3, - 4), C (0,0) are known, then the area of △ ABC is () Just say the answer
• 2. In the rectangular coordinate system, the area of △ ABC can be obtained from the vertices a (- 2,0), B (2,4), C (5,0) of △ ABC
• 3. In the rectangular coordinate system shown in the figure, the vertex coordinates of △ ABC are a (2,0) B (- 1, - 4) C (3, - 3) respectively, and the area is calculated
• 4. As shown in the figure, △ abd and △ ace are both RT △ where ∠ abd = ∠ ace = 90 ° C is on AB, connecting De, and M is the midpoint of de. verification: MC = MB
• 5. As shown in the figure, △ ABC is an isosceles triangle, ∠ ACB = 90 °, extend AB to F, so that ∠ ECF = 135 °. Verification: AE: EC = Ba: CF
• 6. The △ ACB is an isosceles triangle, ∠ ACB = 90 ° extend Ba to e, extend AB to F, ∠ ECF = 135 ° Q: is there an equivalent relationship between AB, AE and BF
• 7. In △ ABC, ab = AC, CG ⊥ Ba intersects the extension line of BA at point g. an isosceles right triangle ruler is placed as shown in Figure 1. The right angle vertex of the triangle ruler is F. one right angle side is in a straight line with AC side, and the other right angle side just passes through point B (1) In Figure 1, please guess and write down the quantitative relationship between BF and CG by observing and measuring the length of BF and CG, and then prove your conjecture; (2) when the triangle ruler moves to the position shown in Figure 2 along the direction of AC, one right angle side is still on the same line with AC side, the other right angle side intersects BC side at point D, and makes de ⊥ BA at point e through point D. at this time, please observe and measure De, D The length of F and CG, conjecture and write the quantitative relationship between de + DF and CG, and then prove your conjecture; (3) whether the conjecture in (2) is still true when the triangle ruler continues to move to the position shown in Fig. 3 along the direction of AC on the basis of (2) (the point F is on the line AC, and the point F does not coincide with point C) (do not explain the reason)
• 8. Δ ABC is isosceles right triangle, ∠ BAC = 90 °, D is a point on AC, extend Ba to e, make AE = ad, prove BD perpendicular to CE
• 9. If P and Q are the triangles of the hypotenuse BC, then Tan ∠ PAQ =?
• 10. E. If f is the trisection of the hypotenuse of ABC, then Tan angle EFC =? I'm sorry. I'm asking for tanecf
• 11. As shown in the figure: vertex a of triangle ABC is on line Mn, triangle ABC rotates around point a, be is perpendicular to Mn at e, CD is perpendicular to Mn at D, and F is the midpoint of BC
• 12. Given the vector OA = (1, K), the vector ob = (K + 1., 2), and the vector OC = (3,1), if the triangle ABC is an isosceles right triangle, then what is k
• 13. In the right triangle ABC, ∠ B = 90 °, OA = OC, OB = 1 / 2Ac On AC
• 14. In the isosceles right triangle ABC, o point to OA = 2, OB = 4, OC = 6. Calculate the angle COA = 135 degrees
• 15. As shown in the figure, O is an internal point of △ ABC, a'b'c 'is on OA, OB and OC respectively, and AB / / a'B', AC / / a'B ', verify that △ ABC is similar to △ a "b'c'
• 16. In the rectangular coordinate system, the vertex a (- 1,5), B (9,5) and point C of the right triangle ABC are on the x-axis, and the coordinates of point C are obtained In the rectangular coordinate system, the vertex a (- 1,5), B (9,5) and point C of the right triangle ABC are on the x-axis, and the coordinates of point C are obtained There are three cases
• 17. In the rectangular coordinate system, a (1,0), B (- 1,0), △ ABC are isosceles right triangles, AB is the bottom, and the area of △ ABC is 1, then the coordinates of point C are equal
• 18. Let a coordinate (2,1) be an isosceles right triangle at a point B in the rectangular coordinate system, and determine the coordinates of point B Write the reason
• 19. The triangle ABC is an isosceles right triangle, in which the angle a is 90 degrees and the length BC is 6. Establish an appropriate right angle coordinate system, and write out the coordinates of each vertex The abscissa of each vertex is increased by 2, and the ordinate remains unchanged. Compared with the original pattern, what is the change of the pattern? 3. If the abscissa of each vertex in 1 is unchanged and the ordinate is - 1, what is the change of the pattern? 4 the abscissa of each vertex in 1 is - 2, and the ordinate remains unchanged. Compared with the original pattern, what is the change of the pattern
• 20. In the rectangular coordinate system, a (1,0), B (- 1,0), △ ABC are isosceles right triangles, then the coordinate of point C is ()