# Test: Coordinate Geometry I - Challenging

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Question 1:   Plot the following points: $A\left(1,2\right),B\left(7,2\right),C\left(1,6\right)$. Connect the points in an alphabetical order and find the area of the figure in square units
$A△=29$
$A△=24$
$A△=12$
$A△=17$
Question 2:   Plot the following points:$A\left(-3,-1\right),B\left(1,-5\right),C\left(7,1\right),D\left(3,5\right)$. Connect the points in an alphabetical order and find the area of the figure in square units
$54$
$36$
$40$
$48$
Question 3:   Plot the following points:$A\left(-4,-3\right),B\left(6,-3\right),C\left(4,2\right),\left(-2,2\right)$. Connect the points in an alphabetical order. Find the area of the figure in square units
$A▱=20$
$A▱=60$
$A▱=40$
$A▱=80$
Question 4:   What is the length of the line connecting the following points: $A\left(5,2\right)$ and $B\left(9,1\right)$
$\sqrt{17}$
$\sqrt{26}$
$13$
$11$
Question 5:   What is the length of the line connecting the following points: $A\left(-2,3\right)$ and $B\left(4,5\right)$
$6$
$\sqrt{68}$
$10$
$2\sqrt{10}$
Question 6:   What is the length of the line connecting points: $P\left(-4,-7\right)$ and $Q\left(1,8\right)$
$20$
$7\sqrt{10}$
$18$
$5\sqrt{10}$
Question 7:   Find the midpoint of the line $PQ$ where $P\left(1,2\right)$, $Q\left(5,4\right)$
$\left(3,3\right)$
$\left(3,2\right)$
$\left(6,6\right)$
$\left(6,3\right)$
Question 8:   Find the midpoint of the line $PQ$ where $P\left(-3,5\right)$, $Q\left(7,12\right)$
$\left(8.5,2\right)$
$\left(9,3\right)$
$\left(2,8.5\right)$
$\left(3,9\right)$
Question 9:   Find the midpoint of the line $PQ$ where $P\left(-5,-7\right)$, $Q\left(-1,-10\right)$
$\left(-3,1.5\right)$
$\left(-2,1.5\right)$
$\left(-3,-8.5\right)$
$\left(-3,8.5\right)$
Question 10:   Find the equation of the straight line whith the points $A\left(-1,-1\right),B\left(2,1\right)$
$y=-\frac{1}{3}x+1$
$y=\frac{1}{3}x+\frac{1}{3}$
$y=\frac{3}{4}x-\frac{1}{5}$
$y=\frac{2}{3}x-\frac{1}{3}$