• 2021 December(E23) Math Question 51

    Similar Triangles & Types of Triangles

    - Similar Triangles

    Similar Triangles
    Choice D
    51. In the standard (x,y) coordinate plane below, point A has coordinates (2,−4), and point B(8,−1) divides AC ___ so that the ratio AB:BC is 1:3. What are the coordinates of point C ?
    AB:BC=1:3AB:BC=1:3
    =>{AB}{AC}={1}{4}=> \frac\{AB\}\{AC\}=\frac\{1\}\{4\}
    {AD}{AE}={AB}{AC}={1}{4}\frac\{AD\}\{AE\}=\frac\{AB\}\{AC\}=\frac\{1\}\{4\}
    {AD}{AE}={1}{4}\frac\{AD\}\{AE\}=\frac\{1\}\{4\}
    {8−2}{AE}={1}{4}=>AE=4×6=24\frac\{8-2\}\{AE\}=\frac\{1\}\{4\}=> AE=4 \times 6=24

    Therefore, the x coordinate of C is 2+24=26.

    {DB}{EC}={AB}{AC}={1}{4}\frac\{DB\}\{EC\}=\frac\{AB\}\{AC\}=\frac\{1\}\{4\}
    {DB}{EC}={1}{4}\frac\{DB\}\{EC\}=\frac\{1\}\{4\}
    {3}{EC}={1}{4}=>EC=12\frac\{3\}\{EC\}=\frac\{1\}\{4\}=> EC=12

    Therefore, the y coordinate of C is -4+12=8.

    The coordinates of point C is (26,8).

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