Question

14. Solutions to this question by accurate drawing will not be accepted y A(-10,-1) D 0 B(0,p) C(7,0) X T(3,-2) The diagram shows a parallelogram ABCD where AB is parallel to DC and DA is parallel to CB. T is a point on DC such that angle BTC is 90°. A is (-10,-1), C is (7,0) and T is (3,-2) The point B lies on the y-axis with coordinates (0, p), where p is a positive constant. (i) Express the gradient of AB and the gradient of BT in terms of p. (ii) Hence, or otherwise, find the value of p. (iii) Find the coordinates of D. (iv) Calculate the perimeter of ABCD, correct to 1 decimal place. (v) By finding the length of BT or otherwise, calculate the area of ABCD.

          14. Solutions to this question by accurate drawing will not be accepted
y
A(-10,-1)
D
0
B(0,p)
C(7,0)
X
T(3,-2)
The diagram shows a parallelogram ABCD where AB is parallel to DC and DA is
parallel to CB. T is a point on DC such that angle BTC is 90°. A is (-10,-1), C is
(7,0) and T is (3,-2)
The point B lies on the y-axis with coordinates (0, p), where p is a positive constant.
(i) Express the gradient of AB and the gradient of BT in terms of p.
(ii) Hence, or otherwise, find the value of p.
(iii) Find the coordinates of D.
(iv) Calculate the perimeter of ABCD, correct to 1 decimal place.
(v) By finding the length of BT or otherwise, calculate the area of ABCD.

14. Solutions to this question by accurate drawing will not be accepted
y
A(-10,-1)
D
0
B(0,p)
C(7,0)
X
T(3,-2)
The diagram shows a parallelogram ABCD where AB is parallel to DC and DA is
parallel to CB. T is a point on DC such that angle BTC is 90°. A is (-10,-1), C is
(7,0) and T is (3,-2)
The point B lies on the y-axis with coordinates (0, p), where p is a positive constant.
(i) Express the gradient of AB and the gradient of BT in terms of p.
(ii) Hence, or otherwise, find the value of p.
(iii) Find the coordinates of D.
(iv) Calculate the perimeter of ABCD, correct to 1 decimal place.
(v) By finding the length of BT or otherwise, calculate the area of ABCD.

Added by Robert D.

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