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this is a grade 10 analytical geometry
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question and it's taken from June 2024
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mid- exam paper So let's jump into it
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Question one reads as follows In the
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figure below A is given by the points -5
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and 2 while B is given as the coordinate
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4 and -2 which are the points on the
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line segment AB Question 1.1 we are
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supposed determine the length of AB Now
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we can use the distance formula to find
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the length of AB The distance formula is
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the square root of the difference of the
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x coordinates squared plus the
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difference of the ycoordinates squared
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as square roo of x a - x b all^ 2 +
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y - y all^ 2 So we can write that out
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like this The length of a b is the
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square of -5 - 4 all^ 2 + 2 -2
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all^ 2 So that's the of -9 2 + 4 2
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So that's the of 81 + 16 which is
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Question 1.2 We are supposed to
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determine the coordinates of the
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midpoint of AB So we assume the midpoint
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M of the line passing through points A
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and B And we know the coordinates of
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point A is given by the points -5 and 2
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while B is given as the coordinate 4 and
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-2 which are the points on the line
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Segment A is shown in the figure Now we
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know that the midpoint formula is this X
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A + XB / 2 Y + Y all over two And this
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is for finding the midpoint when you
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have two points A and B the coordinates
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of two points The student found -1 and
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-2 Let's see whether he is correct or
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not So we can write this out like this
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We have the midpoint mab and we know
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that a is -5 and 2 while b is given as
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the coordinate 4 and -2 So we can
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substitute these values into this
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midpoint formula We'll do that right now
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-5 + 4 for all over 2 and 2 + -2 all
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over 2 We know that negative 5 + 4 for
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all over 2 is equals to -1 / 2 and 2 - 2
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all over 2 is 0 So the coordinates of
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the midpoint of a b will be -1 /2 and 0
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not -2 Question 1.3 we are supposed
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determine the gradient of line A The
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gradient of a line passing through two
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points A and B And we know the
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coordinates of point A is given by the
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points -5 and 2 while B is given as the
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coordinate 4 and -2 The gradient of X a
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YA and XB Y is given by this formula y -
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y all over x a - xb So we can substitute
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our values in the formula So we have the
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gradient of a b is 2 -2 to all over -5 -
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4 which is -4 over 9 This is a grade 10
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analytical geometry question and it's a
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tough one So let's take a look at it now
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And if you have any questions please
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leave them in the comments below and
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I'll see you next time
